Browsing by Author "Maji, B."

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An asymptotic expansion for a Lambert series associated to the symmetric square L -function
(World Scientific, 2023) Juyal, A.; Maji, B.; Sathyanarayana, S.
Hafner and Stopple proved a conjecture of Zagier that the inverse Mellin transform of the symmetric square L-function associated to the Ramanujan tau function has an asymptotic expansion in terms of the nontrivial zeros of the Riemann zeta function ζ(s). Later, Chakraborty et al. extended this phenomenon for any Hecke eigenform over the full modular group. In this paper, we study an asymptotic expansion of the Lambert series ykn=1∞λ f(n2)exp(-ny),as y → 0+, where λf(n) is the nth Fourier coefficient of a Hecke eigenform f(z) of weight k over the full modular group. © 2023 World Scientific Publishing Company.
An Asymptotic Expansion for a Twisted Lambert Series Associated to a Cusp Form and the Möbius Function: Level Aspect
(Birkhauser, 2022) Maji, B.; Sathyanarayana, S.; Shankar, B.R.
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. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
An exact formula for a Lambert series associated to a cusp form and the Möbius function
(Springer, 2022) Juyal, A.; Maji, B.; Sathyanarayana, S.
In 1981, Zagier conjectured that the constant term of the automorphic form y12| Δ (z) | 2, that is, a0(y):=y12∑n=1∞τ2(n)exp(-4πny), where τ(n) is the nth Fourier coefficient of the Ramanujan cusp form Δ (z) , has an asymptotic expansion when y→ 0 + and it can be expressed in terms of the non-trivial zeros of the Riemann zeta function ζ(s). This conjecture was settled by Hafner and Stopple, and later Chakraborty, Kanemitsu, and the second author have extended this result for any Hecke eigenform over the full modular group. In this paper, we investigate a Lambert series associated to the Fourier coefficients of a cusp form and the Möbius function μ(n). We present an exact formula for the Lambert series and interestingly the main term is in terms of the non-trivial zeros of ζ(s) , and the error term is expressed as an infinite series involving the generalized hypergeometric series 2F1(a, b; c; z). As an application of this exact form, we also establish an asymptotic expansion of the Lambert series. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.