Analytic Number Theory
Publisher: Prentice-Hall
Published: 1971
Place of publication: Englewood Cliffs, N.J
Language: eng
Format: Hardcover
Number of pages: 282
Copyright date: 1971
Subjects: Algebraic number theory
Notes: Bibliography: p. 277-278.
Table of contents: label: 1
title: Historical Introduction,
pagenum: 1; label: Part 1
title: Algebraic Number Theory; label: 2
title: The ring of integers of a number field,
pagenum: 9; label: 2-1
title: Integers,
pagenum: 9; label: 2-2
title: Ideal theory,
pagenum: 13; label: 3
title: The locally compact groups of number theory,
pagenum: 20; label: 3-1
title: Completions,
pagenum: 20; label: 3-2
title: Adeles,
pagenum: 32; label: 3-3
title: Ideles,
pagenum: 38; label: 4
title: Local fields,
pagenum: 46; label: 4-1
title: The topology of local fields,
pagenum: 46; label: 4-2
title: Completions of number fields are local fields,
pagenum: 52; label: 4-3
title: The arithmetic of local fields,
pagenum: 55; label: 4-4
title: Local ramification theory,
pagenum: 62; label: 4-5
title: Local Hilbert theory,
pagenum: 67; label: 5
title: Global arithmetic,
pagenum: 72; label: 5-1
title: Splitting of primes,
pagenum: 72; label: 5-2
title: The valuations of an algebraic number field,
pagenum: 79; label: 5-3
title: Global ramification theory,
pagenum: 80; label: 5-4
title: Galois actions,
pagenum: 82; label: 5-5
title: Global Hilbert theory,
pagenum: 84; label: 5-6
title: An example—quadratic fields,
pagenum: 88; label: 6
title: Applications,
pagenum: 93; label: 6-1
title: Special functions,
pagenum: 93; label: 6-2
title: Cyclotomic extensions,
pagenum: 96; label: Part 2
title: Harmonic Analysis; label: 7
title: Harmonic analysis on locally compact abelian groups,
pagenum: 111; label: 7-1
title: Duality theory,
pagenum: 111; label: 7-2
title: Fourier transforms,
pagenum: 121; label: 7-3
title: The Schwartz-Bruhat space,
pagenum: 127; label: Part 3
title: Hecke's L-functions; label: 8
title: Hecke's L-series,
pagenum: 133; label: 8-1
title: Local zeta functions,
pagenum: 133; label: 8-2
title: Global zeta functions,
pagenum: 145; label: 8-3
title: Hecke L-series,
pagenum: 156; label: 9
title: Applications of Hecke L-functions,
pagenum: 162; label: 9-1
title: Splitting of pries,
pagenum: 162; label: 9-2
title: Abelian L-functions,
pagenum: 164; label: 9-3
title: Tchebotarev's density theorem
pagenum: 168; label: 9-4
title: Dirichlet's L-functions,
pagenum: 171; label: 9-5
title: Class number formulas,
pagenum: 172; label: Part 4
title: Class Field Theory; label: 10
title: Class field theory,
pagenum: 181; label: 10-1
title: Abelian L-functions are Hecke L-functions,
pagenum: 182; label: 11
title: The inequalities of class field theory,
pagenum: 188; label: 11-1
title: The second inequality,
pagenum: 188; label: 11-2
title: The first inequality,
pagenum: 197; label: 12
title: Class field theory,
pagenum: 206; label: 12-1
title: Proof of the reciprocity law,
pagenum: 206; label: 12-2
title: Local class field theory,
pagenum: 218; label: 12-3
title: Global class field theory,
pagenum: 226; label: 13
title: Applications,
pagenum: 238; label: 13-1
title: Kronecker's theorem,
pagenum: 238; label: 13-2
title: The power reciprocity law,
pagenum: 241; label: Part 5
title: The Prime Number Theorem; label: 14
title: The prime number theorem,
pagenum: 251; label: 14-1
title: Natural densities,
pagenum: 251; label: 14-2
title: Analytic preliminaries,
pagenum: 257; label: 14-3
title: The prime number theorem,
pagenum: 260; title: Suggestions for further reading,
pagenum: 273; title: Appendix: algebraic preliminaries,
pagenum: 275; title: Bibliography,
pagenum: 277; title: Index,
pagenum: 279