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arXiv · 2405.17205

An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree $n$

Babita·Abhash Kumar Jha·Bibekananda Maji·Manidipa Pal
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Abstract

Utilizing inverse Mellin transform of the symmetric square $L$-function attached to Ramanujan tau function, Hafner and Stopple proved a conjecture of Zagier, which states that the constant term of the automorphic function $y^{12}|\Delta(z)|^2$ i.e., the Lambert series $y^{12}\sum_{n=1}^\infty \tau(n)^2 e^{-4 \pi n y}$ can be expressed in terms of the non-trivial zeros of the Riemann zeta function. This study examines certain Lambert series associated to Siegel cusp forms of degree $n$ twisted by a character $\chi$ and observes a similar phenomenon.

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Babita, Abhash Kumar Jha, Bibekananda Maji, Manidipa Pal. 2024-05-27. An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree $n$. https://arxiv.org/abs/2405.17205

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