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Zeta Functions, Topology and Quantum Physics.

Author: Takashi Aoki; Shigeru Kanemitsu; Mikio Nakahara
Publisher: Dordrecht : Springer, 2008.
Series: Developments in Mathematics, 14.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Focuses on various aspects of zeta functions: multiple zeta values, Ohno's relations, the Riemann hypothesis, L-functions, polylogarithms, and their interplay with other disciplines. Each article starts with an introductory survey leading to the research developments accomplished by the contributors.
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Genre/Form: Conference papers and proceedings
Electronic books
Congresses
Additional Physical Format: Print version:
Aoki, Takashi.
Zeta Functions, Topology and Quantum Physics.
Dordrecht : Springer, ©2008
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Takashi Aoki; Shigeru Kanemitsu; Mikio Nakahara
ISBN: 9780387249810 0387249818
OCLC Number: 828800852
Description: 1 online resource (232 pages).
Contents: Preface; Conference schedule; List of participants; Göllnitz-Gordon Partitions with weights and Parity Conditions; 1 Introduction; 2 A new weighted partition theorem; 3 Series representations; 4 A new infinite hierarchy; Acknowledgments; References; Partition Identities for the Multiple Zeta Function; 1 Introduction; 2 Definitions; 3 Rational Functions; 4 Stuffles and Partition Identities; References; A Perturbative theory of the evolution of the center of typhoons; 1 Introduction; 2 Dynamics of vortex square-root type singularities and Hugonlot-Maslov chains. 3 Equation for the smooth and singular part of the solution Cauchy-Riemann conditions4 Derivation of the Hugonlot-Maslov chain using complex variables and its integrals; Acknowledgments; References; Algebraic Aspects of Multiple Zeta Values; 1 Introduction; 2 The Shuffle Algebra; 3 The Harmonic Algebra and Quasi-Symmetric Functions; 4 Derivations and an Action by Quasi-Symmetric Functions; 5 Cyclic Derivations; 6 Finite Multiple Sums and Mod p Results; References; On the local factor of the zeta function of quadratic orders; Acknowledgments; References. Sums involving the Hurwitz zeta-function values1 Introduction and statement of results; 2 Proof of results; References; Crystal Symmetry Viewed as Zeta Symmetry; 1 Introduction; 2 Lattice zeta-functions and Epstein zeta-functions; 3 Abel means and screened Coulomb potential; References; Sum relations for multiple zeta values; 1 Introduction; 2 Generalizations of the sum formula; 3 Identities associated with Arakawa-Kaneko zeta functions; 4 Multiple zeta-star values and restriction on weight, depth, and height; Acknowledgment; References. The Sum Formula for Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation1 Introduction; Acknowledgment; 2 Shuffle Algebra; 3 Multiple Polylogarithms and the formal KZ equation; 4 Mellin transforms of polylogarithms and the sum formula for MZVs; 5 Knizhnik-Zamolodchikov equation over the configuration space X3 (C); References; Zeta functions over zeros of general zeta and L-functions; 1 Generalities; 2 The first family; 3 The second family; 4 The third family; 5 Concrete examples; References; Hopf Algebras and Transcendental Numbers. 1 Transcendence exponential polynomials and commutative linear algebraic groups2 Bicommutative Hopf algebras; 3 Hopf algebras and multiple zeta values; References.
Series Title: Developments in Mathematics, 14.

Abstract:

Focuses on various aspects of zeta functions: multiple zeta values, Ohno's relations, the Riemann hypothesis, L-functions, polylogarithms, and their interplay with other disciplines. Each article starts with an introductory survey leading to the research developments accomplished by the contributors.

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