Hebrew University
 
Amitsur Algebra Seminar
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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>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Konstantin Golubev   <kgolubev@gmail.com>