Twisted Kronecker series and periods of modular forms on $\Gamma_0(N)$

Clifford Blakestad; YoungJu Choie

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arXiv · 2404.06016

Twisted Kronecker series and periods of modular forms on $\Gamma_0(N)$

Clifford Blakestad·YoungJu Choie

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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 ${\Gamma}_0(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.

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Clifford Blakestad, YoungJu Choie. 2024-04-09. Twisted Kronecker series and periods of modular forms on $\Gamma_0(N)$. https://arxiv.org/abs/2404.06016

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