Correlation between primes in short intervals on curves over finite fields

Seminar
Speaker
Dr. Efrat Bank (University of Michigan)
Date
03/01/2018 - 11:30 - 10:30Add to Calendar 2018-01-03 10:30:00 2018-01-03 11:30:00 Correlation between primes in short intervals on curves over finite fields In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields.  I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial setting.  I will give a sketch of the proof which includes a computation of a certain Galois group, and a counting argument, namely, a Chebotarev density type theorem.    This is a joint work with Tyler Foster. Third floor seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room
Abstract

In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields. 

I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial setting. 

I will give a sketch of the proof which includes a computation of a certain Galois group, and a counting argument, namely, a Chebotarev density type theorem. 

 

This is a joint work with Tyler Foster.

Last Updated Date : 27/11/2017