Tel Aviv University, Colloquium
The next colloquium talk will be held on:
Monday, 29/4/2013, 12:15, Schreiber 006, Tel Aviv University.
Speaker: Lior Bary-Soroker (Tel Aviv University)
Title: Prime polynomials in arithmetic progressions
The abstract is given below. Tea and coffee at 12:00, same room.
Hope to see you there. For information about future colloquia, see
Abstract: 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
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.
Technion Math Net-2 (TECHMATH2)
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