Speaker
Laurent Montaigu
(IMB)
Description
The aim of this talk is to study Kloosterman sums, defined for a prime number $p$ by
$$
K(a,1;p)=\sum_{x\in\mathbb{F}_p^{\times}} e^{\frac{2i\pi(ax+x^{-1})}{p}}.
$$
These sums play a central role in analytic number theory. In particular, we will investigate their statistical behavior as $a$ varies, and present an equidistribution result showing that they asymptotically follow the semicircular law.