A~$p$-arton model for modular cusp forms
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 1, pp. 101-124
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@article{TMF_2021_209_1_a5,
author = {P. Dutta and D. Ghoshal},
title = {A~$p$-arton model for modular cusp forms},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {101--124},
publisher = {mathdoc},
volume = {209},
number = {1},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_1_a5/}
}
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/