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Dimension formulae for the vector spaces of Siegel cusp forms of degree three (II) / / Minking Eie
Dimension formulae for the vector spaces of Siegel cusp forms of degree three (II) / / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Providence, Rhode Island, United States : , : American Mathematical Society, , 1987
Descrizione fisica 1 online resource (134 p.)
Disciplina 510
Collana Memoirs of the American Mathematical Society
Soggetto topico Cusp forms (Mathematics)
Selberg trace formula
Integrals
Soggetto genere / forma Electronic books.
ISBN 1-4704-0793-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""TABLE OF CONTENTS""; ""LIST OF NOTATIONS""; ""INTRODUCTION ""; ""CHAPTER I: FIXED POINTS AND CONJUGACY OF REGULAR ELLIPTIC ELEMENTS IN Sp(3, Z)""; ""1.1 Introduction""; ""1.2 Notations and basic results""; ""1.3 Reducible cases""; ""1.4 Symplectic embeddings of Q(e[(2Ï€i/9)]) and Q(e[(2Ï€i/7)])""; ""1.5 Application""; ""CHAPTER II: CONJUGACY CLASSES OF THE MODULAR GROUP Sp(3, Z)""; ""2.1 Introduction""; ""2.2 Basic results""; ""2.3 Conjugacy classes of Î?[sup(2)][sub(3)]""; ""2.4 Conjugacy classes of Î?[sup(1)][sub(3)]""; ""2.5 Conjugacy classes of Î?[sup(3)][sub(0)]""
""2.6 Applications and further remarks""""CHAPTER III: EXPLICIT EVALUATIONS""; ""3.1 Introduction""; ""3.2 Contributions from conjugacy classes of regular elliptic elements""; ""3.3 Contribution from conjugacy classes in Î?[sup(2)][sub(3)]""; ""3.4 Contributions from conjugacy classes in Î?[sup(1)][sub(3)]""; ""3.5 Contributions from conjugacy classes in Î?[sup(0)][sub(3)]""; ""3.6 An explicit dimension formula for Siegel cusp forms of degree three""; ""3.7 Autemorphic forms of degree three and its generating function""
""CHAPTER IV: DIMENSION FORMULAE FOR THE VECTOR SPACES OF SIEGEL CUSP FORMS OF DEGREE THREE""""4.1 Introduction""; ""4.2 Eie's results""; ""4.3 Conjugacy classes of Sp(3, Z)""; ""4.4 The main terms""; ""4.5 Determination of C[sub(1)], C[sub(2)] and C[sub(3)]""; ""4.6 The partial fractions of the generating function""; ""4.7 The generating function for modular form of degree four""; ""REFERENCES""
Record Nr. UNINA-9910480578303321
Eie Minking <1952->  
Providence, Rhode Island, United States : , : American Mathematical Society, , 1987
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Dimension formulae for the vector spaces of Siegel cusp forms of degree three (II) / / Minking Eie
Dimension formulae for the vector spaces of Siegel cusp forms of degree three (II) / / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Providence, Rhode Island, United States : , : American Mathematical Society, , 1987
Descrizione fisica 1 online resource (134 p.)
Disciplina 510
Collana Memoirs of the American Mathematical Society
Soggetto topico Cusp forms (Mathematics)
Selberg trace formula
Integrals
ISBN 1-4704-0793-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""TABLE OF CONTENTS""; ""LIST OF NOTATIONS""; ""INTRODUCTION ""; ""CHAPTER I: FIXED POINTS AND CONJUGACY OF REGULAR ELLIPTIC ELEMENTS IN Sp(3, Z)""; ""1.1 Introduction""; ""1.2 Notations and basic results""; ""1.3 Reducible cases""; ""1.4 Symplectic embeddings of Q(e[(2Ï€i/9)]) and Q(e[(2Ï€i/7)])""; ""1.5 Application""; ""CHAPTER II: CONJUGACY CLASSES OF THE MODULAR GROUP Sp(3, Z)""; ""2.1 Introduction""; ""2.2 Basic results""; ""2.3 Conjugacy classes of Î?[sup(2)][sub(3)]""; ""2.4 Conjugacy classes of Î?[sup(1)][sub(3)]""; ""2.5 Conjugacy classes of Î?[sup(3)][sub(0)]""
""2.6 Applications and further remarks""""CHAPTER III: EXPLICIT EVALUATIONS""; ""3.1 Introduction""; ""3.2 Contributions from conjugacy classes of regular elliptic elements""; ""3.3 Contribution from conjugacy classes in Î?[sup(2)][sub(3)]""; ""3.4 Contributions from conjugacy classes in Î?[sup(1)][sub(3)]""; ""3.5 Contributions from conjugacy classes in Î?[sup(0)][sub(3)]""; ""3.6 An explicit dimension formula for Siegel cusp forms of degree three""; ""3.7 Autemorphic forms of degree three and its generating function""
""CHAPTER IV: DIMENSION FORMULAE FOR THE VECTOR SPACES OF SIEGEL CUSP FORMS OF DEGREE THREE""""4.1 Introduction""; ""4.2 Eie's results""; ""4.3 Conjugacy classes of Sp(3, Z)""; ""4.4 The main terms""; ""4.5 Determination of C[sub(1)], C[sub(2)] and C[sub(3)]""; ""4.6 The partial fractions of the generating function""; ""4.7 The generating function for modular form of degree four""; ""REFERENCES""
Record Nr. UNINA-9910788884703321
Eie Minking <1952->  
Providence, Rhode Island, United States : , : American Mathematical Society, , 1987
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Dimension formulae for the vector spaces of Siegel cusp forms of degree three (II) / / Minking Eie
Dimension formulae for the vector spaces of Siegel cusp forms of degree three (II) / / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Providence, Rhode Island, United States : , : American Mathematical Society, , 1987
Descrizione fisica 1 online resource (134 p.)
Disciplina 510
Collana Memoirs of the American Mathematical Society
Soggetto topico Cusp forms (Mathematics)
Selberg trace formula
Integrals
ISBN 1-4704-0793-0
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""TABLE OF CONTENTS""; ""LIST OF NOTATIONS""; ""INTRODUCTION ""; ""CHAPTER I: FIXED POINTS AND CONJUGACY OF REGULAR ELLIPTIC ELEMENTS IN Sp(3, Z)""; ""1.1 Introduction""; ""1.2 Notations and basic results""; ""1.3 Reducible cases""; ""1.4 Symplectic embeddings of Q(e[(2Ï€i/9)]) and Q(e[(2Ï€i/7)])""; ""1.5 Application""; ""CHAPTER II: CONJUGACY CLASSES OF THE MODULAR GROUP Sp(3, Z)""; ""2.1 Introduction""; ""2.2 Basic results""; ""2.3 Conjugacy classes of Î?[sup(2)][sub(3)]""; ""2.4 Conjugacy classes of Î?[sup(1)][sub(3)]""; ""2.5 Conjugacy classes of Î?[sup(3)][sub(0)]""
""2.6 Applications and further remarks""""CHAPTER III: EXPLICIT EVALUATIONS""; ""3.1 Introduction""; ""3.2 Contributions from conjugacy classes of regular elliptic elements""; ""3.3 Contribution from conjugacy classes in Î?[sup(2)][sub(3)]""; ""3.4 Contributions from conjugacy classes in Î?[sup(1)][sub(3)]""; ""3.5 Contributions from conjugacy classes in Î?[sup(0)][sub(3)]""; ""3.6 An explicit dimension formula for Siegel cusp forms of degree three""; ""3.7 Autemorphic forms of degree three and its generating function""
""CHAPTER IV: DIMENSION FORMULAE FOR THE VECTOR SPACES OF SIEGEL CUSP FORMS OF DEGREE THREE""""4.1 Introduction""; ""4.2 Eie's results""; ""4.3 Conjugacy classes of Sp(3, Z)""; ""4.4 The main terms""; ""4.5 Determination of C[sub(1)], C[sub(2)] and C[sub(3)]""; ""4.6 The partial fractions of the generating function""; ""4.7 The generating function for modular form of degree four""; ""REFERENCES""
Record Nr. UNINA-9910828912403321
Eie Minking <1952->  
Providence, Rhode Island, United States : , : American Mathematical Society, , 1987
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Dimensions of spaces of Siegel cusp forms of degree two and three / / Minking Eie
Dimensions of spaces of Siegel cusp forms of degree two and three / / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Providence, Rhode Island, United States : , : American Mathematical Society, , 1984
Descrizione fisica 1 online resource (194 p.)
Disciplina 512/.72
Collana Memoirs of the American Mathematical Society
Soggetto topico Cusp forms (Mathematics)
Selberg trace formula
Integrals
Soggetto genere / forma Electronic books.
ISBN 1-4704-0717-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""2.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (I)""""2.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (II)""; ""2.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points""; ""2.6 Contributions from conjugacy classes of unipotent elements""; ""2.7 A dimension formula for the vector space of cusp forms with respect to Sp (2 , Z)""; ""CHAPTER III: REPRESENTATIVES OF CONJUGACY CLASSES OF ELEMENTS OF Sp (3 , Z) IN Sp (3 , R)""; ""3.1 Introduction""
""4.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points""""4.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points""; ""4.6 Second case of conjugacy classes of elements having a one-dimensional set of fixed points""; ""4.7 Second case of conjugacy classes of elements having a two-dimensional set of fixed points""; ""CHAPTER V: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Î?[sub(0)]""; ""5.1 Introduction""; ""5.2 A dimension formula for the principal congruencesubgroup Î?[sub(2)](N)""
""5.3 Contributions from Î?[sub(0)](I)""""5.4 A dimension formula for the principal congruence subgroup Î?[sub(3)](N)""; ""5.5 Contributions from Î?[sub(0)](II)""; ""5.6 A final remark""; ""REFERENCES""
Record Nr. UNINA-9910480533703321
Eie Minking <1952->  
Providence, Rhode Island, United States : , : American Mathematical Society, , 1984
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Dimensions of spaces of Siegel cusp forms of degree two and three / / Minking Eie
Dimensions of spaces of Siegel cusp forms of degree two and three / / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Providence, Rhode Island, United States : , : American Mathematical Society, , 1984
Descrizione fisica 1 online resource (194 p.)
Disciplina 512/.72
Collana Memoirs of the American Mathematical Society
Soggetto topico Cusp forms (Mathematics)
Selberg trace formula
Integrals
ISBN 1-4704-0717-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""2.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (I)""""2.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (II)""; ""2.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points""; ""2.6 Contributions from conjugacy classes of unipotent elements""; ""2.7 A dimension formula for the vector space of cusp forms with respect to Sp (2 , Z)""; ""CHAPTER III: REPRESENTATIVES OF CONJUGACY CLASSES OF ELEMENTS OF Sp (3 , Z) IN Sp (3 , R)""; ""3.1 Introduction""
""4.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points""""4.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points""; ""4.6 Second case of conjugacy classes of elements having a one-dimensional set of fixed points""; ""4.7 Second case of conjugacy classes of elements having a two-dimensional set of fixed points""; ""CHAPTER V: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Î?[sub(0)]""; ""5.1 Introduction""; ""5.2 A dimension formula for the principal congruencesubgroup Î?[sub(2)](N)""
""5.3 Contributions from Î?[sub(0)](I)""""5.4 A dimension formula for the principal congruence subgroup Î?[sub(3)](N)""; ""5.5 Contributions from Î?[sub(0)](II)""; ""5.6 A final remark""; ""REFERENCES""
Record Nr. UNINA-9910788887803321
Eie Minking <1952->  
Providence, Rhode Island, United States : , : American Mathematical Society, , 1984
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Dimensions of spaces of Siegel cusp forms of degree two and three / / Minking Eie
Dimensions of spaces of Siegel cusp forms of degree two and three / / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Providence, Rhode Island, United States : , : American Mathematical Society, , 1984
Descrizione fisica 1 online resource (194 p.)
Disciplina 512/.72
Collana Memoirs of the American Mathematical Society
Soggetto topico Cusp forms (Mathematics)
Selberg trace formula
Integrals
ISBN 1-4704-0717-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto ""2.3 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (I)""""2.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points (II)""; ""2.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points""; ""2.6 Contributions from conjugacy classes of unipotent elements""; ""2.7 A dimension formula for the vector space of cusp forms with respect to Sp (2 , Z)""; ""CHAPTER III: REPRESENTATIVES OF CONJUGACY CLASSES OF ELEMENTS OF Sp (3 , Z) IN Sp (3 , R)""; ""3.1 Introduction""
""4.4 Contributions from conjugacy classes of elements having a one-dimensional set of fixed points""""4.5 Contributions from conjugacy classes of elements having a two-dimensional set of fixed points""; ""4.6 Second case of conjugacy classes of elements having a one-dimensional set of fixed points""; ""4.7 Second case of conjugacy classes of elements having a two-dimensional set of fixed points""; ""CHAPTER V: CONTRIBUTIONS FROM CONJUGACY CLASSES IN Î?[sub(0)]""; ""5.1 Introduction""; ""5.2 A dimension formula for the principal congruencesubgroup Î?[sub(2)](N)""
""5.3 Contributions from Î?[sub(0)](I)""""5.4 A dimension formula for the principal congruence subgroup Î?[sub(3)](N)""; ""5.5 Contributions from Î?[sub(0)](II)""; ""5.6 A final remark""; ""REFERENCES""
Record Nr. UNINA-9910828763803321
Eie Minking <1952->  
Providence, Rhode Island, United States : , : American Mathematical Society, , 1984
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Theory of multiple Zeta values with applications in combinatorics [[electronic resource] /] / Minking Eie
Theory of multiple Zeta values with applications in combinatorics [[electronic resource] /] / Minking Eie
Autore Eie Minking <1952->
Pubbl/distr/stampa Hackensack, NJ, : World Scientific Pub., c2013
Descrizione fisica 1 online resource (313 p.)
Disciplina 510
512.73
515.56
Collana Monographs in number theory
Soggetto topico Functions, Zeta
Algebraic functions
Soggetto genere / forma Electronic books.
ISBN 981-4472-64-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface; Contents; I Basic Theory of Multiple Zeta Values; 0 The Time Before Multiple Zeta Values; 0.1 The Evaluation of Euler Double Sums; 0.2 Vandermonde Convolution; 0.3 Zeta Functions Associated with Multiple Zeta Values; 0.4 Messages from Modular Forms; 1 Introduction to the Theory of Multiple Zeta Values; 1.1 Introduction and Notations; 1.2 Drinfeld Integral Representations of Multiple Zeta Values; 1.3 Double Weighted Sum Formulas; 1.4 The Expectations of Binomial Distributions; 1.5 Exercises; 2 The Sum Formula; 2.1 Through the Integral Representations
2.2 Another Proof of the Sum Formula2.3 Evaluation of Multiple Zeta Values of Height One; 2.4 Exercises; II Shuffle Relations among Multiple Zeta Values; 3 Some Shuffle Relations; 3.1 Shuffle Relations of Multiple Zeta Values; 3.2 An Application of Double Weighted Sums; 3.3 Shuffle Relations of Two Sums of Multiple Zeta Values; 3.4 A Vector Version of the Restricted Sum Formula; 3.5 Exercises; 4 Euler Decomposition Theorem; 4.1 A Shuffle Relation with Two Parameters; 4.2 Integrals with Three Factors; 4.3 Generalizations of Euler Decomposition Theorem
4.4 Applications of the Decomposition Theorem4.5 Applications of Another Decomposition Theorem; 4.6 Exercises; 5 Multiple Zeta Values of Height Two; 5.1 Sums of Multiple Zeta Values of Height Two; 5.2 Weighted Sums of Multiple Zeta Values of Height Two; 5.3 The Shuffle Product Formula of a Sum and Others; 5.4 Exercises; III Applications of Shuffle Relations in Combinatorics; 6 Generalizations of Pascal Identity; 6.1 Applications of Shuffle Products in Combinatorics; 6.2 Hypergeometric Distribution; 6.3 The Generating Function of Three Variables; 6.4 Exercises
7 Combinatorial Identities of Convolution Type7.1 Some Particular Combinatorial Identities; 7.2 A Generating Function for Products; 7.3 A Combinatorial Identity of Convolution Type; 7.4 Another Generating Function of Three Variables; 7.5 Exercises; 8 Vector Versions of Some Combinatorial Identities; 8.1 The Shuffle Product of Two Sums; 8.2 More Combinatorial Identities of Convolution Type; 8.3 Vector Versions of Pascal Identity; 8.4 Problems on Combinatorial Identity; Appendices; A Singular Modular Forms on the Exceptional Domain; A.1 Cayley Numbers and Integral Cayley Numbers
A.2 The Exceptional DomainA.3 The Theory of Jacobi Forms; A.4 A Final Application; Appendix (i): Jacobi Forms over Cayley Numbers; Appendix (ii): Basic Properties of a Set of Theta Series; B Shuffle Product Formulas of Multiple Zeta Values; B.1 Introduction; B.2 The Shuffle Product Formula of Two Multiple Zeta Values; B.3 Some Basic Shuffle Relations; B.4 Shuffle Relations of Two Sums of Multiple Zeta Values; B.5 The Generating Function of Height One; Appendix (i): Double Weighted Sum Formulas; Appendix (ii): Evaluations of Some Particular Integrals
C The Sum Formula and Their Generalizations
Record Nr. UNINA-9910452281303321
Eie Minking <1952->  
Hackensack, NJ, : World Scientific Pub., c2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The theory of multiple zeta values with applications in combinatorics / / Minking Eie, National Chung Cheng University, Taiwan
The theory of multiple zeta values with applications in combinatorics / / Minking Eie, National Chung Cheng University, Taiwan
Autore Eie Minking <1952->
Pubbl/distr/stampa Hackensack, NJ, : World Scientific Pub., c2013
Descrizione fisica 1 online resource (xii, 300 pages) : illustrations
Disciplina 510
512.73
515.56
Collana Monographs in number theory
Soggetto topico Functions, Zeta
Functions of complex variables
Combinatorial analysis
ISBN 981-4472-64-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface; Contents; I Basic Theory of Multiple Zeta Values; 0 The Time Before Multiple Zeta Values; 0.1 The Evaluation of Euler Double Sums; 0.2 Vandermonde Convolution; 0.3 Zeta Functions Associated with Multiple Zeta Values; 0.4 Messages from Modular Forms; 1 Introduction to the Theory of Multiple Zeta Values; 1.1 Introduction and Notations; 1.2 Drinfeld Integral Representations of Multiple Zeta Values; 1.3 Double Weighted Sum Formulas; 1.4 The Expectations of Binomial Distributions; 1.5 Exercises; 2 The Sum Formula; 2.1 Through the Integral Representations
2.2 Another Proof of the Sum Formula2.3 Evaluation of Multiple Zeta Values of Height One; 2.4 Exercises; II Shuffle Relations among Multiple Zeta Values; 3 Some Shuffle Relations; 3.1 Shuffle Relations of Multiple Zeta Values; 3.2 An Application of Double Weighted Sums; 3.3 Shuffle Relations of Two Sums of Multiple Zeta Values; 3.4 A Vector Version of the Restricted Sum Formula; 3.5 Exercises; 4 Euler Decomposition Theorem; 4.1 A Shuffle Relation with Two Parameters; 4.2 Integrals with Three Factors; 4.3 Generalizations of Euler Decomposition Theorem
4.4 Applications of the Decomposition Theorem4.5 Applications of Another Decomposition Theorem; 4.6 Exercises; 5 Multiple Zeta Values of Height Two; 5.1 Sums of Multiple Zeta Values of Height Two; 5.2 Weighted Sums of Multiple Zeta Values of Height Two; 5.3 The Shuffle Product Formula of a Sum and Others; 5.4 Exercises; III Applications of Shuffle Relations in Combinatorics; 6 Generalizations of Pascal Identity; 6.1 Applications of Shuffle Products in Combinatorics; 6.2 Hypergeometric Distribution; 6.3 The Generating Function of Three Variables; 6.4 Exercises
7 Combinatorial Identities of Convolution Type7.1 Some Particular Combinatorial Identities; 7.2 A Generating Function for Products; 7.3 A Combinatorial Identity of Convolution Type; 7.4 Another Generating Function of Three Variables; 7.5 Exercises; 8 Vector Versions of Some Combinatorial Identities; 8.1 The Shuffle Product of Two Sums; 8.2 More Combinatorial Identities of Convolution Type; 8.3 Vector Versions of Pascal Identity; 8.4 Problems on Combinatorial Identity; Appendices; A Singular Modular Forms on the Exceptional Domain; A.1 Cayley Numbers and Integral Cayley Numbers
A.2 The Exceptional DomainA.3 The Theory of Jacobi Forms; A.4 A Final Application; Appendix (i): Jacobi Forms over Cayley Numbers; Appendix (ii): Basic Properties of a Set of Theta Series; B Shuffle Product Formulas of Multiple Zeta Values; B.1 Introduction; B.2 The Shuffle Product Formula of Two Multiple Zeta Values; B.3 Some Basic Shuffle Relations; B.4 Shuffle Relations of Two Sums of Multiple Zeta Values; B.5 The Generating Function of Height One; Appendix (i): Double Weighted Sum Formulas; Appendix (ii): Evaluations of Some Particular Integrals
C The Sum Formula and Their Generalizations
Record Nr. UNINA-9910779883003321
Eie Minking <1952->  
Hackensack, NJ, : World Scientific Pub., c2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
The theory of multiple zeta values with applications in combinatorics / / Minking Eie, National Chung Cheng University, Taiwan
The theory of multiple zeta values with applications in combinatorics / / Minking Eie, National Chung Cheng University, Taiwan
Autore Eie Minking <1952->
Pubbl/distr/stampa Hackensack, NJ, : World Scientific Pub., c2013
Descrizione fisica 1 online resource (xii, 300 pages) : illustrations
Disciplina 510
512.73
515.56
Collana Monographs in number theory
Soggetto topico Functions, Zeta
Functions of complex variables
Combinatorial analysis
ISBN 981-4472-64-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface; Contents; I Basic Theory of Multiple Zeta Values; 0 The Time Before Multiple Zeta Values; 0.1 The Evaluation of Euler Double Sums; 0.2 Vandermonde Convolution; 0.3 Zeta Functions Associated with Multiple Zeta Values; 0.4 Messages from Modular Forms; 1 Introduction to the Theory of Multiple Zeta Values; 1.1 Introduction and Notations; 1.2 Drinfeld Integral Representations of Multiple Zeta Values; 1.3 Double Weighted Sum Formulas; 1.4 The Expectations of Binomial Distributions; 1.5 Exercises; 2 The Sum Formula; 2.1 Through the Integral Representations
2.2 Another Proof of the Sum Formula2.3 Evaluation of Multiple Zeta Values of Height One; 2.4 Exercises; II Shuffle Relations among Multiple Zeta Values; 3 Some Shuffle Relations; 3.1 Shuffle Relations of Multiple Zeta Values; 3.2 An Application of Double Weighted Sums; 3.3 Shuffle Relations of Two Sums of Multiple Zeta Values; 3.4 A Vector Version of the Restricted Sum Formula; 3.5 Exercises; 4 Euler Decomposition Theorem; 4.1 A Shuffle Relation with Two Parameters; 4.2 Integrals with Three Factors; 4.3 Generalizations of Euler Decomposition Theorem
4.4 Applications of the Decomposition Theorem4.5 Applications of Another Decomposition Theorem; 4.6 Exercises; 5 Multiple Zeta Values of Height Two; 5.1 Sums of Multiple Zeta Values of Height Two; 5.2 Weighted Sums of Multiple Zeta Values of Height Two; 5.3 The Shuffle Product Formula of a Sum and Others; 5.4 Exercises; III Applications of Shuffle Relations in Combinatorics; 6 Generalizations of Pascal Identity; 6.1 Applications of Shuffle Products in Combinatorics; 6.2 Hypergeometric Distribution; 6.3 The Generating Function of Three Variables; 6.4 Exercises
7 Combinatorial Identities of Convolution Type7.1 Some Particular Combinatorial Identities; 7.2 A Generating Function for Products; 7.3 A Combinatorial Identity of Convolution Type; 7.4 Another Generating Function of Three Variables; 7.5 Exercises; 8 Vector Versions of Some Combinatorial Identities; 8.1 The Shuffle Product of Two Sums; 8.2 More Combinatorial Identities of Convolution Type; 8.3 Vector Versions of Pascal Identity; 8.4 Problems on Combinatorial Identity; Appendices; A Singular Modular Forms on the Exceptional Domain; A.1 Cayley Numbers and Integral Cayley Numbers
A.2 The Exceptional DomainA.3 The Theory of Jacobi Forms; A.4 A Final Application; Appendix (i): Jacobi Forms over Cayley Numbers; Appendix (ii): Basic Properties of a Set of Theta Series; B Shuffle Product Formulas of Multiple Zeta Values; B.1 Introduction; B.2 The Shuffle Product Formula of Two Multiple Zeta Values; B.3 Some Basic Shuffle Relations; B.4 Shuffle Relations of Two Sums of Multiple Zeta Values; B.5 The Generating Function of Height One; Appendix (i): Double Weighted Sum Formulas; Appendix (ii): Evaluations of Some Particular Integrals
C The Sum Formula and Their Generalizations
Record Nr. UNINA-9910815775303321
Eie Minking <1952->  
Hackensack, NJ, : World Scientific Pub., c2013
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui