A Course in Arithmetic / Edition 1

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Overview

Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.
From the reviews: "... The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems." American Scientist
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Product Details

  • ISBN-13: 9780387900407
  • Publisher: Springer New York
  • Publication date: 4/18/1973
  • Series: Graduate Texts in Mathematics Series , #7
  • Edition description: 1st Corrected ed. 1973. Corr. 3rd printing 1996
  • Edition number: 1
  • Pages: 118
  • Sales rank: 865,494
  • Product dimensions: 0.44 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

I—Algebraic Methods.- I—Finite fields.- 1—Generalities.- 2—Equations over a finite field.- 3—Quadratic reciprocity law.- Appendix—Another proof of the quadratic reciprocity law.- II — p-adic fields.- 1—The ring Zp and the field Qp.- 2—p-adic equations.- 3—The multiplicative group of Qp.- III—Hilbert symbol.- 1—Local properties.- 2—Global properties.- IV—Quadratic forms over Qp and over Q.- 1—Quadratic forms.- 2—Quadratic forms over Qp.- 3—Quadratic forms over Q.- Appendix—Sums of three squares.- V—Integral quadratic forms with discriminant ± 1.- 1—Preliminaries.- 2—Statement of results.- 3—Proofs.- II—Analytic Methods.- VI—The theorem on arithmetic progressions.- 1—Characters of finite abelian groups.- 2—Dirichlet series.- 3—Zeta function and L functions.- 4—Density and Dirichlet theorem.- VII—Modular forms.- 1—The modular group.- 2—Modular functions.- 3—The space of modular forms.- 4—Expansions at infinity.- 5—Hecke operators.- 6—Theta functions.- Index of Definitions.- Index of Notations.

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