Small Algebraic Central Values of Twists of Elliptic L-Functions

2020/01/10 by Kisilevsky, Hershy, Nam, Jungbae
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.03547

Abstract

We consider heuristic predictions for small non-zero algebraic central values of twists of the L-function of an elliptic curve E/ℚ by Dirichlet characters. We provide computational evidence for these predictions and consequences of them for instances of an analogue of the Brauer-Siegel theorem associated to E/ℚ extended to chosen families of cyclic extensions of fixed degree.

Related

• L-values of elliptic curves twisted by cubic characters
• On Twists of A Family of Elliptic Curves and Their L-Function
• Vanishing of L-functions of elliptic curves over number fields
• Horizontal p-adic L-functions
• Multiple Dirichlet series predictions for moments of L-functions: unitary, symplectic and orthogonal examples