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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 FieldsEdit

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 FieldsEdit

Hilbert SymbolEdit

Quadratic Forms Over Q p and Q Edit

Integral Quadratic Forms with Discriminant ±1 Edit

The Theorem on Arithmetic ProgressionsEdit

Modular FormsEdit

ReferencesEdit