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arXiv · 2310.01127

Real-analytic modular forms for $\Gamma_0(N)$ and their $L$-series

Joshua Drewitt·Joshua Pimm
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Abstract

We introduce an $L$-series associated to real-analytic modular forms which transform with weight $(r,s)\in\mathbb{Z}^2$ under $\Gamma_0(N)$. These $L$-series satisfy a functional equation and converse theorem. We also discuss examples of such forms, including real analytic Eisenstein series and modular iterated integrals of higher level. We focus on the $L$-series for a class of forms including Francis Brown's length-one modular iterated integrals $\mathcal{MI}^!_1$.

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Joshua Drewitt, Joshua Pimm. 2023-10-02. Real-analytic modular forms for $\Gamma_0(N)$ and their $L$-series. https://arxiv.org/abs/2310.01127

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