A $p$-arton Model for Modular Cusp Forms

Parikshit Dutta; Debashis Ghoshal

doi:10.1134/s0040577921100068

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arXiv · 2103.02443

A $p$-arton Model for Modular Cusp Forms

Parikshit Dutta·Debashis Ghoshal

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Abstract

We propose to associate to a modular form (an infinite number of) complex valued functions on the $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. We elaborate on the correspondence and study its consequence in terms of the Mellin transforms and the $L$-functions related to the forms. Further we discuss the case of products of Dirichlet $L$-functions and their Mellin duals, which are convolution products of $\vartheta$-series. The latter are intriguingly similar to non-holomorphic Maass forms of weight zero as suggested by their Fourier coefficients.

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Parikshit Dutta, Debashis Ghoshal. 2021-02-26. A $p$-arton Model for Modular Cusp Forms. https://doi.org/10.1134/s0040577921100068

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