LEADER 05315nam 2200697Ia 450 001 9910452281303321 005 20200520144314.0 010 $a981-4472-64-6 035 $a(CKB)2550000001096041 035 $a(EBL)1275552 035 $a(OCoLC)854975165 035 $a(SSID)ssj0001104227 035 $a(PQKBManifestationID)11685599 035 $a(PQKBTitleCode)TC0001104227 035 $a(PQKBWorkID)11088536 035 $a(PQKB)11264095 035 $a(MiAaPQ)EBC1275552 035 $a(WSP)00008769 035 $a(PPN)189428457 035 $a(Au-PeEL)EBL1275552 035 $a(CaPaEBR)ebr10731517 035 $a(CaONFJC)MIL502616 035 $a(EXLCZ)992550000001096041 100 $a20130717d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTheory of multiple Zeta values with applications in combinatorics$b[electronic resource] /$fMinking Eie 210 $aHackensack, NJ, $cWorld Scientific Pub.$dc2013 215 $a1 online resource (313 p.) 225 0 $aMonographs in number theory ;$vv.7 300 $aDescription based upon print version of record. 311 $a981-4472-63-8 311 $a1-299-71365-3 320 $aIncludes bibliographical references and index. 327 $aPreface; 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 327 $a2.2 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 327 $a4.4 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 327 $a7 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 327 $aA.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 327 $aC The Sum Formula and Their Generalizations 330 $aThis is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, producing numerous interesting identities that are ready to be used. This will provide a powerful tool to deal with problems in multiple zeta values, both in evaluations and shuffle relations. The volume will benefit graduate students doing research in number theory. 410 0$aMonographs in Number Theory 606 $aFunctions, Zeta 606 $aAlgebraic functions 608 $aElectronic books. 615 0$aFunctions, Zeta. 615 0$aAlgebraic functions. 676 $a510 676 $a512.73 676 $a515.56 700 $aEie$b Minking$f1952-$0899499 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910452281303321 996 $aTheory of multiple Zeta values with applications in combinatorics$92256521 997 $aUNINA