"Theorem of
Primes on Arithmetic Progression"

By

**ALÝ ADALI**

**(Bilkent
University) **

Abstract: The aim of the talk is to prove the theorem called
“primes on arithmetic progression”, which was conjectured and used by Legendre and proved by Dirichlet.
The theorem briefly states that there are infinitely many primes congruent to a
modulo m when relatively prime integers a and m given.

The proof is based on the usage of Dirichlet series, some analytic properties of the Riemann
zeta function, and some algebraic properties of Dirichlet
L-functions.

**Date: ****Thursday, September 28, 2006**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room, SAZ-141**