Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, April 29, 2013

Schreiber 006, 12:15

Lior Bary-Soroker

Tel Aviv University

Prime polynomials in arithmetic progressions

There is an analogy between Z, the ring of integers, and F_q[t],
the ring of polynomials over a finite field with q elements.
We will demonstrate this analogy through the following problem
about prime numbers in arithmetic progression:

Let x>0 and d a modulus. The Prime Number Theorem for arithmetic progressions
asserts that if x is sufficiently large and if d is fixed, then the primes p<x equi-distribute
amongst the arithmetic progressions p = a(mod d), where gcd(a,d)=1.
In many applications it is crucial to allow d to grow with x, so the problem
`how big can d be so that equi-distribution is still satisfied' is naturally raised.
(Under the Generalized Riemann Hypothesis one can take d^(2+delta)<x,
and it is conjectured that we can take d^(1+delta)<x.)

This talk is based on a joint work with Efrat Bank and Lior Rosenzweig.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006