Corpus ID: 237635090

# An asymptotic expansion for a twisted Lambert series associated to a cusp form and the M\"{o}bius function: level aspect

@inproceedings{Maji2021AnAE,
title={An asymptotic expansion for a twisted Lambert series associated to a cusp form and the M\"\{o\}bius function: level aspect},
author={Bibekananda Maji and Sumukha Sathyanarayana and B. R. Shankar},
year={2021}
}
• Published 24 September 2021
• Mathematics
Recently, Juyal, Maji and Sathyanarayana have studied a Lambert series associated with a cusp form over the full modular group and the Möbius function. In this paper, we investigate the Lambert series ∑ ∞ n=1[af (n)ψ(n)∗μ(n)ψ′(n)] exp(−ny), where af (n) is the nth Fourier coefficient of a cusp form f over any congruence subgroup, and ψ and ψ are primitive Dirichlet characters. This extends the earlier work to the case of higher level subgroups and also gives a character analogue.

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