A User's Guide to Serre's Arithmetic/The Theorem on Arithmetic Progressions

< A User's Guide to Serre's Arithmetic

Characters of Finite Abelian Groups

Duality

Orthogonality Relations

Modular Characters

Proposition 5 uses a couple clever tricks:

$\varepsilon :(2\mathbb {N} +1,\cdot )\to (\mathbb {Z} /2,+)$ is a monoid morphism
$x\equiv 1{\text{ }}({\text{mod }}4l_{1}\cdots l_{k})$ implies $x\equiv 1{\text{ }}({\text{mod }}4)$ and $x\equiv 1{\text{ }}({\text{mod }}l_{i})$

Dirichlet Series

Lemmas

Dirichlet Series

Dirichlet Series with Positive Coefficients

Ordinary Dirichlet Series

Zeta Functions and L-Functions

Eulerian Products

The Zeta Function

The L-Functions

Product of the L-Functions Related to the Same $m$

Density and the Dirichlet Theorem

Density

Lemmas

Proof of Theorem 2

An Applications

Natural Density

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