Sums of two squares in function fields

יום ד', 21/10/2015 - 11:00
Fermat was the first to characterize which integer numbers are sums of two perfect squares. A natural question of analytical number theory is: How many integers up to x are of that form? Landau settled this question using Dirichlet series and complex analysis.
We'll discuss Landau's proof and present recent results on the corresponding problem over the rational function field over a finite field, which requires new ideas.