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2017•International Journal of Number TheoryRequires access

An asymptotic expansion of a Lambert series associated to cusp forms

Kalyan Sekhar Chakraborty, Abhishek Juyal, Shiv Datt Kumar, Bibekananda Maji

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Abstract

Zagier’s conjecture on the asymptotic expansion of the Lambert series [Formula: see text] where [Formula: see text] is the Ramanujan’s tau function, was proved by Hafner and Stopple. Recently, Chakraborty, Kanemitsu and Maji have extended this result to any cusp forms over the full modular group. The goal of this paper is to extend the asymptotic behavior to cusp forms over any congruence subgroup of the full modular group.

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What this paper is about

Zagier’s conjecture on the asymptotic expansion of the Lambert series [Formula: see text] where [Formula: see text] is the Ramanujan’s tau function, was proved by Hafner and Stopple. Recently, Chakraborty, Kanemitsu and Maji have extended this result to any cusp forms over the full modular group. The goal of this paper is to extend the asymptotic behavior to cusp forms over any congruence subgroup of the full modular group.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Zagier’s conjecture on the asymptotic expansion of the Lambert series [Formula: see text] where [Formula: see text] is the Ramanujan’s tau function, was proved by Hafner and Stopple. Recently, Chakraborty, Kanemitsu and Maji have extended this result to any cusp forms over the full modular group. The goal of this paper is to extend the asymptotic behavior to cusp forms over any congruence subgroup of the full modular group.

Key concepts: Cusp (singularity), Mathematics, Cusp form, Ramanujan's sum, Modular form, Conjecture, Congruence (geometry), Congruence subgroup

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