School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

Tel Aviv University

There is an analogy between Z, the ring of integers, and F_q[t],

Abstract:

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