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.
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.
 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 Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of padic measures; the EulerMaclaurin 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 polyBernoulli 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
 Language
 eng
 Extent
 XI, 274 pages 5 illustrations, 1 illustrations in color.
 Isbn
 9784431549192
 Label
 Bernoulli Numbers and Zeta Functions
 Title
 Bernoulli Numbers and Zeta Functions
 Statement of responsibility
 by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko
 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 Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of padic measures; the EulerMaclaurin 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 polyBernoulli 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
 Cataloging source
 ITFiEUI
 http://library.link/vocab/creatorName
 Arakawa, Tsuneo
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Ibukiyama, Tomoyoshi.
 Kaneko, Masanobu.
 SpringerLink (Online service)
 Series statement

 Springer Monographs in Mathematics,
 Springer eBooks
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 Global analysis (Mathematics)
 Number theory
 Label
 Bernoulli Numbers and Zeta Functions, by Tsuneo Arakawa, Tomoyoshi Ibukiyama, Masanobu Kaneko, (electronic resource)
 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
 9784431549192
 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, noncommercial 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
 10.1007/9784431549192
 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)
 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
 9784431549192
 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, noncommercial 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
 10.1007/9784431549192
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086461470
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