# Modular forms, Eisenstein series and the ternary divisor function

30 January 2014
16:00
Emmanuel Kowalski
Abstract
<p><span>After a short survey of the notion of level of distribution for </span><br /><span>arithmetic functions, and its importance in analytic number theory, we</span><br /><span> will explain how our recent studies of twists of Fourier coefficients of </span><br /><span>modular forms (and especially Eisenstein series) by "trace functions" </span><br /><span>lead to an improvement of the results of Friedlander-Iwaniec and</span><br /><span> Heath-Brown for the ternary divisor function in arithmetic progressions</span><br /><span> to prime moduli.</span></p> <p><span>This is&nbsp;<span>joint work with É. Fouvry and Ph. Michel.</span></span></p>
• Number Theory Seminar