An edition of Analytic number theory (1971)

Analytic Number Theory

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Cover of: Analytic Number Theory by Larry Joel Goldstein
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Last edited by Stew
August 30, 2022 | History
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An edition of Analytic number theory (1971)

Analytic Number Theory

by

  • 0 Ratings
  • 2 Want to read
  • 1 Currently reading
  • 0 Have read

This text is the result of a course offered at the University of Maryland College Park in the 1970's. A FREE pdf version is available online...just BING-it!

Publish Date
Publisher
Prentice-Hall
Language
English
Pages
282

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Previews available in: English

Subjects
Algebraic number theory, Handbooks, manuals, Social sciences, Statistical methods, Computer programs, Statistics, Data processing, Processamento eletrônico de dados, Ciências sociais, SPSS, Guides, manuels, Sciences sociales, Logiciels, Méthodes statistiques, Statistique, Informatique, SPSS (Computer file), SPSS (Logiciel)

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Cover of: Analytic Number Theory
Analytic Number Theory
1971, Prentice-Hall
Hardcover in English

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Book Details

Table of Contents

1. Historical Introduction, Page 1
Part 1. Algebraic Number Theory
2. The ring of integers of a number field, Page 9 2-1. Integers, Page 9 2-2. Ideal theory, Page 13 3. The locally compact groups of number theory, Page 20 3-1. Completions, Page 20 3-2. Adeles, Page 32 3-3. Ideles, Page 38 4. Local fields, Page 46 4-1. The topology of local fields, Page 46 4-2. Completions of number fields are local fields, Page 52 4-3. The arithmetic of local fields, Page 55 4-4. Local ramification theory, Page 62 4-5. Local Hilbert theory, Page 67 5. Global arithmetic, Page 72 5-1. Splitting of primes, Page 72 5-2. The valuations of an algebraic number field, Page 79 5-3. Global ramification theory, Page 80 5-4. Galois actions, Page 82 5-5. Global Hilbert theory, Page 84 5-6. An example—quadratic fields, Page 88 6. Applications, Page 93 6-1. Special functions, Page 93 6-2. Cyclotomic extensions, Page 96
Part 2. Harmonic Analysis
7. Harmonic analysis on locally compact abelian groups, Page 111 7-1. Duality theory, Page 111 7-2. Fourier transforms, Page 121 7-3. The Schwartz-Bruhat space, Page 127
Part 3. Hecke's L-functions
8. Hecke's L-series, Page 133 8-1. Local zeta functions, Page 133 8-2. Global zeta functions, Page 145 8-3. Hecke L-series, Page 156 9. Applications of Hecke L-functions, Page 162 9-1. Splitting of pries, Page 162 9-2. Abelian L-functions, Page 164 9-3. Tchebotarev's density theorem Page 168 9-4. Dirichlet's L-functions, Page 171 9-5. Class number formulas, Page 172
Part 4. Class Field Theory
10. Class field theory, Page 181 10-1. Abelian L-functions are Hecke L-functions, Page 182 11. The inequalities of class field theory, Page 188 11-1. The second inequality, Page 188 11-2. The first inequality, Page 197 12. Class field theory, Page 206 12-1. Proof of the reciprocity law, Page 206 12-2. Local class field theory, Page 218 12-3. Global class field theory, Page 226 13. Applications, Page 238 13-1. Kronecker's theorem, Page 238 13-2. The power reciprocity law, Page 241
Part 5. The Prime Number Theorem
14. The prime number theorem, Page 251 14-1. Natural densities, Page 251 14-2. Analytic preliminaries, Page 257 14-3. The prime number theorem, Page 260 Suggestions for further reading, Page 273 Appendix: algebraic preliminaries, Page 275 Bibliography, Page 277 Index, Page 279

Edition Notes

Bibliography: p. 277-278.

Published in
Englewood Cliffs, N.J
Copyright Date
1971

Classifications

Dewey Decimal Class
512/.73
Library of Congress
QA247 .G67, HA32 .S6345 2001

The Physical Object

Format
Hardcover
Pagination
xv, 282 p.
Number of pages
282

ID Numbers

Open Library
OL4577208M
Internet Archive
analyticnumberth00gold_0
LCCN
77140688
Amazon ID (ASIN)
B000QTW6N4

Source records

Scriblio MARC record
University of Prince Edward Island MARC record
Internet Archive item record
Library of Congress MARC record
Library of Congress MARC record

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August 30, 2022 Edited by Stew Update covers
December 17, 2020 Edited by MARC Bot import existing book
November 5, 2013 Edited by David M. Dyer Edited without comment.
April 28, 2010 Edited by Open Library Bot Linked existing covers to the work.
December 9, 2009 Created by WorkBot add works page