Cruz A. Castillo

Affiliation: University of Illinois Urbana Champaign

Title Of Talk: Non-vanishing for quartic Hecke $L$-functions and elliptic curve $L$-functions

URLS:
https://arxiv.org/abs/2509.12078

Abstract: We show that a positive proportion of Hecke L-functions attached to the quartic residue symbol modulo squarefree Gaussian integers do not vanish at the central point. Our method also extends to the Hecke characters associated to squarefree quartic twists of the congruent number elliptic curve over the Gaussian field. In particular, we prove that a positive proportion (ordered by norm) of squarefree quartic twists of the congruent number elliptic curve over the Gaussian field have Mordell-Weil rank 0. This is joint work with Alexandre de Faveri and Alexander Dunn.

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