The denominator of twisted $L$-values of elliptic curves

Abstract: In the context of the generalised Birch and Swinnerton-Dyer conjecture, one considers the value at $s=1$ of the L-function of an elliptic curve $E/\mathbb{Q}$ twisted by a Dirichlet character $\chi$. When normalised with a period, one obtains an algebraic number $\mathscr{L}(E,\chi)$. I will discuss the question under what conditions $\mathscr{L}(E,\chi)$ is an algebraic integer and what the possible denominators could be.

number theory

Audience: researchers in the topic

Algebra and Number Theory Seminars at Université Laval