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# Efrat Bank : Primes in short intervals on curves over finite fields.

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 a count, and will give a rough sketch of the proof. This is a joint work with Tyler Foster.

**Category**: Number Theory**Duration**: 01:34:45**Date**: February 22, 2017 at 3:10 PM**Views**: 107-
**Tags:**seminar, Number Theory Seminar

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