Primes in short intervals on curves over finite fields

Abstract: We prove an analogue of the Prime Number Theorem for short intervals on a smooth proper curve of arbitrary genus over a finite field. Our main result gives a uniform asymptotic count of those rational functions, inside short intervals defined by a very ample effective divisor E, whose principal divisors are prime away from E.
In this talk, I will discuss the setting and definitions we use in order to make sense of such count, and will give a rough sketch of the proof.

This is a joint work with Tyler Foster.