Zeta Functions, Topology and Quantum Physics

Krishnaswami Alladi, Alexander Berkovich (auth.), Takashi Aoki, Shigeru Kanemitsu, Mikio Nakahara, Yasuo Ohno (eds.)0387249729, 9780387249728, 0387249818

This volume 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.

Eleven articles on recent advances are written by outstanding experts in the above-mentioned fields. Each article starts with an introductory survey leading to the exciting new research developments accomplished by the contributors.

This book will become the major standard reference on the recent advances on zeta functions.

Audience

This book, primarily intended for researchers in number theory and mathematical physics, is also accessible to graduate students in these fields.

Table of contents :
Göllnitz-Gordon Partitions with Weights and Parity Conditions….Pages 1-17
Partition Identities for the Multiple Zeta Function….Pages 19-29
A Perturbative Theory of the Evolution of the Center of Typhoons….Pages 31-50
Algebraic Aspects of Multiple Zeta Values….Pages 51-73
On the Local Factor of the Zeta Function of Quadratic Orders….Pages 75-79
Sums Involving the Hurwitz Zeta-Function Values….Pages 81-90
Crystal Symmetry Viewed as Zeta Symmetry….Pages 91-129
Sum Relations for Multiple Zeta Values….Pages 131-144
The Sum Formula for Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation….Pages 145-170
Zeta Functions Over Zeros of General Zeta and L -Functions….Pages 171-196
Hopf Algebras and Transcendental Numbers….Pages 197-219