Twisted Kronecker series and periods of modular forms on Γ₀(N)

2024/04/09 by Blakestad, Clifford, Choie, YoungJu
#11F12 #11F25 #11F50 #11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2404.06016

Abstract

We introduce an infinite family of Kronecker series twisted by characters. As an application, we give a closed formula for the sum of all Hecke eigenforms on Γ₀(N) multiplied by their twisted period polynomials in terms of the product of those twisted Kronecker series, when N is square free. This extends an identity of Zagier among period polynomials, Hecke eigenforms and a quotient of Jacobi theta series.

Related

• Periods of modular forms on Γ₀(N) and products of Jacobi theta functions
• Periods of Hilbert Modular forms, Kronecker series and Cohomology
• Twisted periods of modular forms
• Twisted Hecke L-values and period polynomials
• Periods of Jacobi forms and Hecke operator