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

Characters of Finite Abelian Groups edit

Duality edit

Orthogonality Relations edit

Modular Characters edit

Proposition 5 uses a couple clever tricks:

  1.   is a monoid morphism
  2.   implies   and  

Dirichlet Series edit

Lemmas edit

Dirichlet Series edit

Dirichlet Series with Positive Coefficients edit

Ordinary Dirichlet Series edit

Zeta Functions and L-Functions edit

Eulerian Products edit

The Zeta Function edit

The L-Functions edit

Product of the L-Functions Related to the Same   edit

Density and the Dirichlet Theorem edit

Density edit

Lemmas edit

Proof of Theorem 2 edit

An Applications edit

Natural Density edit