Period-like polynomials for L-series associated with half-integral weight cusp forms

2023/07/20 by Branch, James, Diamantis, Nikolaos, Raji, Wissam +1
#11F37 #11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2307.10863

Abstract

Given the L-series of a half-integral weight cusp form, we construct a cohomology class with coefficients in a finite dimensional vector space in a way that parallels the Eichler cohomology in the integral weight case. We also define a lift of half-integral weight cusp forms to integral weight modular forms that is compatible with the L-series of the respective forms.

Related

• The Riemann Hypothesis for period polynomials of cusp forms
• Eichler cohomology and zeros of polynomials associated to derivatives of\n L-functions
• Period polynomials, derivatives of L-functions, and zeros of polynomials
• Non-vanishing of L-functions associated to cusp forms of half-integral weight
• Period functions for vector-valued Maass cusp forms of real weight, with an application to Jacobi Maass cusp forms