Zeta Functions, Topology and Quantum Physics

ISBN-13: 9780387249728 / Angielski / Twarda / 2005 / 219 str.

Takashi Aoki; Shigeru Kanemitsu; Mikio Nakahara

Opis

This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Spis treści

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.

Blurb

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.