Zeta Functions, Topology and Quantum Physics [recurso electrónico] / edited by Takashi Aoki, Shigeru Kanemitsu, Mikio Nakahara, Yasuo Ohno.

Göllnitz-Gordon Partitions with Weights and Parity Conditions -- Partition Identities for the Multiple Zeta Function -- A Perturbative Theory of the Evolution of the Center of Typhoons -- Algebraic Aspects of Multiple Zeta Values -- On the Local Factor of the Zeta Function of Quadratic Orders -- Sums Involving the Hurwitz Zeta-Function Values -- Crystal Symmetry Viewed as Zeta Symmetry -- Sum Relations for Multiple Zeta Values -- The Sum Formula for Multiple Zeta Values and Connection Problem of the Formal Knizhnik-Zamolodchikov Equation -- Zeta Functions Over Zeros of General Zeta and L-Functions -- Hopf Algebras and Transcendental Numbers.

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.