# Correlation between primes in short intervals on curves over finite fields

`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`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