The Resource Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, (electronic resource)

# Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, (electronic resource) Resource Information The item Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.

Label
Bernoulli Numbers and Zeta Functions
Title
Bernoulli Numbers and Zeta Functions
Statement of responsibility
by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko
Creator
Contributor
Author
Subject
Language
eng
Summary
Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen--von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler--Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and poly-Bernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new
Member of
IT-FiEUI
Arakawa, Tsuneo
Image bit depth
0
Literary form
non fiction
• Ibukiyama, Tomoyoshi.
• Kaneko, Masanobu.
Series statement
• Springer Monographs in Mathematics,
• Springer eBooks
• Mathematics
• Algebra
• Global analysis (Mathematics)
• Number theory
Label
Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
• txt
Content type MARC source
rdacontent.
Control code
978-4-431-54919-2
Dimensions
unknown
Extent
XI, 274 pages 5 illustrations, 1 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9784431549192
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
• c
Other control number
10.1007/978-4-431-54919-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086461470
Label
Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
• cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
• txt
Content type MARC source
rdacontent.
Control code
978-4-431-54919-2
Dimensions
unknown
Extent
XI, 274 pages 5 illustrations, 1 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9784431549192
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
• c
Other control number
10.1007/978-4-431-54919-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086461470