Bernoulli numbers and zeta functions:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Tokyo [u.a.]
Springer
2014
|
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9784431549185 9784431549192 |
| DOI: | 10.1007/978-4-431-54919-2 |
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Datensatz im Suchindex
| _version_ | 1804152456993570816 |
|---|---|
| adam_text | BERNOULLI NUMBERS AND ZETA FUNCTIONS
/ ARAKAWA, TSUNEO
: 2014
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Arakawa, Tsuneo 1949-2003 Ibukiyama, Tomoyoshi Kaneko, Masanobu |
| author_GND | (DE-588)113768745 |
| author_facet | Arakawa, Tsuneo 1949-2003 Ibukiyama, Tomoyoshi Kaneko, Masanobu |
| author_role | aut aut aut |
| author_sort | Arakawa, Tsuneo 1949-2003 |
| author_variant | t a ta t i ti m k mk |
| building | Verbundindex |
| bvnumber | BV042034338 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)885825885 (DE-599)DNB105359531X |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-4-431-54919-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:11:01Z |
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| language | English |
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| spelling | Arakawa, Tsuneo 1949-2003 Verfasser (DE-588)113768745 aut Bernoulli numbers and zeta functions Tsuneo Arakawa ; Tomoyoshi Ibukiyama ; Masanobu Kaneko Tokyo [u.a.] Springer 2014 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Springer monographs in mathematics Bernoullische Zahl (DE-588)4276648-5 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Bernoullische Zahl (DE-588)4276648-5 s Zetafunktion (DE-588)4190764-4 s Zahlentheorie (DE-588)4067277-3 s 1\p DE-604 Ibukiyama, Tomoyoshi Verfasser aut Kaneko, Masanobu Verfasser aut https://doi.org/10.1007/978-4-431-54919-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027475746&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Arakawa, Tsuneo 1949-2003 Ibukiyama, Tomoyoshi Kaneko, Masanobu Bernoulli numbers and zeta functions Bernoullische Zahl (DE-588)4276648-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Zetafunktion (DE-588)4190764-4 gnd |
| subject_GND | (DE-588)4276648-5 (DE-588)4067277-3 (DE-588)4190764-4 |
| title | Bernoulli numbers and zeta functions |
| title_auth | Bernoulli numbers and zeta functions |
| title_exact_search | Bernoulli numbers and zeta functions |
| title_full | Bernoulli numbers and zeta functions Tsuneo Arakawa ; Tomoyoshi Ibukiyama ; Masanobu Kaneko |
| title_fullStr | Bernoulli numbers and zeta functions Tsuneo Arakawa ; Tomoyoshi Ibukiyama ; Masanobu Kaneko |
| title_full_unstemmed | Bernoulli numbers and zeta functions Tsuneo Arakawa ; Tomoyoshi Ibukiyama ; Masanobu Kaneko |
| title_short | Bernoulli numbers and zeta functions |
| title_sort | bernoulli numbers and zeta functions |
| topic | Bernoullische Zahl (DE-588)4276648-5 gnd Zahlentheorie (DE-588)4067277-3 gnd Zetafunktion (DE-588)4190764-4 gnd |
| topic_facet | Bernoullische Zahl Zahlentheorie Zetafunktion |
| url | https://doi.org/10.1007/978-4-431-54919-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027475746&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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