Hebrew University Amitsur Algebra Seminar ---------------------------------- Time: Thursday, Jun 6, 12:00-13:15 Place: math 209 Title: Prime polynomials in arithmetic progressions Speaker: Lior Bary-Soroker (TAU) 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 (which is an integer). 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. You are cordially invited! <http://ma.huji.ac.il/amitsur.html> --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Konstantin Golubev <kgolubev@gmail.com>