Geodesic
A $p$-arton model for modular cusp forms
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 1, pp. 101-124 Cet article a éte moissonné depuis la source Math-Net.Ru

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To a modular form, we propose to associate (an infinite number of) complex-valued functions on $p$-adic numbers $\mathbb{Q}_p$ for each prime $p$. We elaborate on the correspondence and study its consequences in terms of the Mellin transform and the $L$-function related to the form. 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 nonholomorphic Maass forms of weight zero as suggested by their Fourier coefficients.
Keywords: modular cusp forms, $p$-adic wavelets, theta functions, $L$-functions. 
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P. Dutta; D. Ghoshal. A $p$-arton model for modular cusp forms. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 1, pp. 101-124. http://geodesic.mathdoc.fr/item/TMF_2021_209_1_a5/

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