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A User's Guide to Serre's Arithmetic

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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 | edit source]

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 | edit source]

Hilbert Symbol[edit | edit source]

Quadratic Forms Over Q p and Q [edit | edit source]

Integral Quadratic Forms with Discriminant ±1 [edit | edit source]

The Theorem on Arithmetic Progressions[edit | edit source]

Modular Forms[edit | edit source]

References[edit | edit source]