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

Characters of Finite Abelian GroupsEdit

DualityEdit

Orthogonality RelationsEdit

Modular CharactersEdit

Proposition 5 uses a couple clever tricks:

  1.   is a monoid morphism
  2.   implies   and  

Dirichlet SeriesEdit

LemmasEdit

Dirichlet SeriesEdit

Dirichlet Series with Positive CoefficientsEdit

Ordinary Dirichlet SeriesEdit

Zeta Functions and L-FunctionsEdit

Eulerian ProductsEdit

The Zeta FunctionEdit

The L-FunctionsEdit

Product of the L-Functions Related to the Same  Edit

Density and the Dirichlet TheoremEdit

DensityEdit

LemmasEdit

Proof of Theorem 2Edit

An ApplicationsEdit

Natural DensityEdit