Thursday 18 Jan 2018: NT Seminar: The Function Field Sathe-Selberg Formula - CANCELLED
Ardavan Afshar - University College London (UCL)
In the 1950s Selberg invented an ingenious analytic technique, which would later be developed into the so-called Selberg-Delange method, for enumerating certain arithmetic quantities. In particular, he used it to derive an asymptotic formula, originally due to Sathe, for the number of numbers less than x with exactly k prime factors, uniformly in k (a generalisation of the prime number theorem). We have adapted this technique to the setting of the rational function field over a finite field, where one can eliminate some technicalities and get stronger results, the latter on account of Weil's Riemann Hypothesis for curves over finite fields. We count an analogous quantity to that of Sathe and Selberg, and then refine it to the case of fixed arithmetic progressions or short intervals. This is joint work with Sam Porritt.