Number theory seminar

Cancelled, will be moved to Wednesday


Speaker: Jasper Van Hirtum, KU Leuven and Univ. Luxembourg.

Title: On the distribution of Frobenius of weight 2 eigenforms with quadratic coefficient field.

Abstract: The coefficients of a modular form without so called inner twists are elements of a  totally real number field. If this number field is different from Q then one can study the set of primes p such that the p-th coefficient is a rational number. This set is known to be of density zero. However only conjectural statements exists on its size. Using the latest results on the Sato-Tate conjecture for Abelian varieties we obtain a heuristic model for the asymptotic size of this set under reasonable assumptions. More precisely we treat the case of weight 2 eigenforms with quadratic coefficient field without inner twist. Moreover we present numerical data which agrees with our model and the assumptions we made to obtain it.