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Author:   Tsuneo Arakawa ,  Tomoyoshi Ibukiyama ,  Masanobu Kaneko ,  Don B. Zagier
Publisher:   Springer Verlag, Japan
Imprint:   Springer Verlag, Japan
Edition:   Softcover reprint of the original 1st ed. 2014
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   4.394kg
ISBN:  

9784431563839

ISBN 10:   4431563830
Pages:   274
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

​1. Bernoulli Numbers 2. Stirling Numbers and Bernoulli Numbers3. Theorem of Clausen and von Staudt, and Kummer’s Congruence4. Generalized Bernoulli Numbers5. Summation Formula of Euler–Maclaurin and Riemann Zeta Function 6. Quadratic Forms and Ideal Theory of Quadratic Fields 7. Congruence Between Bernoulli Numbers and Class Numbers of Imaginary Quadratic Fields 8. Character Sums and Bernoulli Numbers 9. Special Values and Complex Integral Representation of L-functions 10. Class Number Formula and an Easy Zeta Function of a Prehomogeneous Vector Space11. p-adic Measure and Kummer’s Congruence12. Hurwitz Numbers 13. The Barnes Multiple Zeta Function14. Poly-Bernoulli NumbersReferencesIndex

Reviews

The book touches on all of the well-known classical results related to Bernoulli numbers and zeta functions ... . The book will offer something to readers at all levels of expertise, from the student of number theory looking for interesting topics to delve into, to researchers looking for an overview of various results, in each case pointing the way to further study. (Luis Manuel Navas Vicente, Mathematical Reviews, October, 2015) This book ... is perhaps the first full-length treatment of these fascinating numbers-certainly the first modern one. ... the book has an interdisciplinary character, offering thorough treatments of the Bernoulli numbers from the optics of the history of mathematics, combinatorics, analytic number theory, and algebraic number theory ... . Summing Up: Highly recommended. Upper-division undergraduates and above. (D. V. Feldman, Choice, Vol. 52 (10), June, 2015) The present book contains some specific material reflecting the research interests of the authors. ... The monograph is a useful addition to the library of every researcher working on special numbers and special functions. (Khristo N. Boyadzhiev, zbMATH 1312.11015, 2015) The book under review is about Bernoulli numbers and zeta functions. ... The main audience for the book are researchers and students studying Bernoulli numbers and related topics. The text of the book is very fluent. Concepts and proofs are introduced in detail, and it is easy to follow for reader. There are some exercises, so the book can be used in a graduate course as well. (Mehdi Hassani, MAA Reviews, December, 2014)

Author Information

(late) Tsuneo Arakawa Tomoyoshi Ibukiyama Professor Department of Mathematics Graduate School of Science Osaka University Machikaneyama 1-1 Toyonaka, Osaka, 560-0043 Japan Masanobu Kaneko Professor Faculty of Mathematics Kyushu University Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan

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