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Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]]
| Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]] |
| Autore | Paris R. B. |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2001 |
| Descrizione fisica | 1 online resource (xvi, 422 pages) : digital, PDF file(s) |
| Disciplina | 515/.723 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Mellin transform
Asymptotic expansions |
| ISBN |
1-107-12112-4
1-280-41805-2 9786610418053 1-139-14661-0 0-511-17409-8 0-511-06706-2 0-511-06075-0 0-511-32800-1 0-511-54666-1 0-511-06919-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Order Relations -- Asymptotic Expansions -- Other Expansions -- Biographies of Mellin and Barnes -- Fundamental Results -- The Gamma Function [Gamma] (z) -- The Asymptotic Expansion of [Gamma] (z) -- The Stirling Coefficients -- Bounds for [Gamma] (z) -- Expansion of Quotients of Gamma Functions -- Inverse Factorial Expansions -- A Recursion Formula when [alpha subscript r] = [beta subscript r] -- An Algebraic Method for the Determination of the A[subscript j] -- Special Cases -- The Asymptotic Expansion of Integral Functions -- Convergence of Mellin-Barnes Integrals -- Order Estimates for Remainder Integrals -- Lemmas -- Properties of Mellin Transforms -- Basic Properties -- Translational and Differential Properties -- The Parseval Formula -- Analytic Properties -- Inverse Mellin Transforms -- Integrals Connected with e[superscript -z] -- Some Standard Integrals -- Discontinuous Integrals -- Gamma-Function Integrals -- Ramanujan-Type Integrals -- Barnes' Lemmas -- Mellin-Barnes Integral Representations -- The Confluent Hypergeometric Functions -- The Gauss Hypergeometric Function -- Some Special Functions -- Applications of Mellin Transforms -- Transformation of Series -- The Mellin Transform Method -- The Poisson-Jacobi Formula -- An Infinite Series -- A Smoothed Dirichlet Series -- A Finite Sum -- Number-Theoretic Examples -- A Harmonic Sum -- Euler's Product -- Ramanujan's Function -- Some Other Number-Theoretic Sums -- Solution of Differential Equations -- Potential Problems in Wedge-Shaped Regions. |
| Altri titoli varianti | Asymptotics & Mellin-Barnes Integrals |
| Record Nr. | UNINA-9910450367603321 |
Paris R. B.
|
||
| Cambridge : , : Cambridge University Press, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]]
| Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]] |
| Autore | Paris R. B. |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2001 |
| Descrizione fisica | 1 online resource (xvi, 422 pages) : digital, PDF file(s) |
| Disciplina | 515/.723 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Mellin transform
Asymptotic expansions |
| ISBN |
1-107-12112-4
1-280-41805-2 9786610418053 1-139-14661-0 0-511-17409-8 0-511-06706-2 0-511-06075-0 0-511-32800-1 0-511-54666-1 0-511-06919-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Order Relations -- Asymptotic Expansions -- Other Expansions -- Biographies of Mellin and Barnes -- Fundamental Results -- The Gamma Function [Gamma] (z) -- The Asymptotic Expansion of [Gamma] (z) -- The Stirling Coefficients -- Bounds for [Gamma] (z) -- Expansion of Quotients of Gamma Functions -- Inverse Factorial Expansions -- A Recursion Formula when [alpha subscript r] = [beta subscript r] -- An Algebraic Method for the Determination of the A[subscript j] -- Special Cases -- The Asymptotic Expansion of Integral Functions -- Convergence of Mellin-Barnes Integrals -- Order Estimates for Remainder Integrals -- Lemmas -- Properties of Mellin Transforms -- Basic Properties -- Translational and Differential Properties -- The Parseval Formula -- Analytic Properties -- Inverse Mellin Transforms -- Integrals Connected with e[superscript -z] -- Some Standard Integrals -- Discontinuous Integrals -- Gamma-Function Integrals -- Ramanujan-Type Integrals -- Barnes' Lemmas -- Mellin-Barnes Integral Representations -- The Confluent Hypergeometric Functions -- The Gauss Hypergeometric Function -- Some Special Functions -- Applications of Mellin Transforms -- Transformation of Series -- The Mellin Transform Method -- The Poisson-Jacobi Formula -- An Infinite Series -- A Smoothed Dirichlet Series -- A Finite Sum -- Number-Theoretic Examples -- A Harmonic Sum -- Euler's Product -- Ramanujan's Function -- Some Other Number-Theoretic Sums -- Solution of Differential Equations -- Potential Problems in Wedge-Shaped Regions. |
| Altri titoli varianti | Asymptotics & Mellin-Barnes Integrals |
| Record Nr. | UNINA-9910783125203321 |
|
Paris R. B.
|
||
| Cambridge : , : Cambridge University Press, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski
| Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski |
| Autore | Paris R. B |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cambridge ; ; New York, : Cambridge University Press, 2001 |
| Descrizione fisica | 1 online resource (xvi, 422 pages) : digital, PDF file(s) |
| Disciplina | 515/.723 |
| Altri autori (Persone) | KaminskiD <1960-> (David) |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Mellin transform
Asymptotic expansions |
| ISBN |
1-107-12112-4
1-280-41805-2 9786610418053 1-139-14661-0 0-511-17409-8 0-511-06706-2 0-511-06075-0 0-511-32800-1 0-511-54666-1 0-511-06919-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Order Relations -- Asymptotic Expansions -- Other Expansions -- Biographies of Mellin and Barnes -- Fundamental Results -- The Gamma Function [Gamma] (z) -- The Asymptotic Expansion of [Gamma] (z) -- The Stirling Coefficients -- Bounds for [Gamma] (z) -- Expansion of Quotients of Gamma Functions -- Inverse Factorial Expansions -- A Recursion Formula when [alpha subscript r] = [beta subscript r] -- An Algebraic Method for the Determination of the A[subscript j] -- Special Cases -- The Asymptotic Expansion of Integral Functions -- Convergence of Mellin-Barnes Integrals -- Order Estimates for Remainder Integrals -- Lemmas -- Properties of Mellin Transforms -- Basic Properties -- Translational and Differential Properties -- The Parseval Formula -- Analytic Properties -- Inverse Mellin Transforms -- Integrals Connected with e[superscript -z] -- Some Standard Integrals -- Discontinuous Integrals -- Gamma-Function Integrals -- Ramanujan-Type Integrals -- Barnes' Lemmas -- Mellin-Barnes Integral Representations -- The Confluent Hypergeometric Functions -- The Gauss Hypergeometric Function -- Some Special Functions -- Applications of Mellin Transforms -- Transformation of Series -- The Mellin Transform Method -- The Poisson-Jacobi Formula -- An Infinite Series -- A Smoothed Dirichlet Series -- A Finite Sum -- Number-Theoretic Examples -- A Harmonic Sum -- Euler's Product -- Ramanujan's Function -- Some Other Number-Theoretic Sums -- Solution of Differential Equations -- Potential Problems in Wedge-Shaped Regions. |
| Record Nr. | UNINA-9910829174103321 |
|
Paris R. B
|
||
| Cambridge ; ; New York, : Cambridge University Press, 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910461830703321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto non controllato |
ArtinГchreier reduced polynomial
Emanuel Kowalski EulerАoincar formula Frobenius conjugacy class Frobenius conjugacy Frobenius tori GoursatЋolchinВibet theorem Kloosterman sheaf Laurent polynomial Legendre Mellin transform Pierre Deligne Ron Evans Tannakian category Tannakian groups Zeeev Rudnick algebro-geometric autodual objects autoduality characteristic two connectedness dimensional objects duality equidistribution exponential sums fiber functor finite field Mellin transform finite field finite fields geometrical irreducibility group scheme hypergeometric sheaf interger monic polynomials isogenies lie-irreducibility lisse middle convolution middle extension sheaf monic polynomial monodromy groups noetherian connected scheme nonsplit form nontrivial additive character number theory odd characteristic odd prime orthogonal case perverse sheaves polynomials pure weight semisimple object semisimple sheaves signs split form supermorse theorem theorems |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910789730903321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto non controllato |
ArtinГchreier reduced polynomial
Emanuel Kowalski EulerАoincar formula Frobenius conjugacy class Frobenius conjugacy Frobenius tori GoursatЋolchinВibet theorem Kloosterman sheaf Laurent polynomial Legendre Mellin transform Pierre Deligne Ron Evans Tannakian category Tannakian groups Zeeev Rudnick algebro-geometric autodual objects autoduality characteristic two connectedness dimensional objects duality equidistribution exponential sums fiber functor finite field Mellin transform finite field finite fields geometrical irreducibility group scheme hypergeometric sheaf interger monic polynomials isogenies lie-irreducibility lisse middle convolution middle extension sheaf monic polynomial monodromy groups noetherian connected scheme nonsplit form nontrivial additive character number theory odd characteristic odd prime orthogonal case perverse sheaves polynomials pure weight semisimple object semisimple sheaves signs split form supermorse theorem theorems |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910824873803321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
