A User's Guide to Serre's Arithmetic

This wikibook is a companion guide to Serre's book on arithmetic. His proofs will be dissected, external references will be made, technique discussed, and computations made

Finite Fields edit

In this chapter Serre studies the basic properties of finite fields. Of them, he gives uniqueness of finite fields   of characteristic   and order  , gives the structure of the group  , discusses solutions of polynomials over finite fields, and gives a necessary and sufficient condition for


to be a field extension or the product ring  .

p-adic Fields edit

Hilbert Symbol edit

Quadratic Forms Over Q p and Q edit

Integral Quadratic Forms with Discriminant ±1 edit

The Theorem on Arithmetic Progressions edit

Modular Forms edit

References edit