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arXiv · 2305.07412

An asymptotic expansion for a Lambert series associated to Siegel cusp forms

Babita·Abhash Kumar Jha·Abhishek Juyal·Bibekananda Maji
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Abstract

In 2000, Hafner and Stopple proved a conjecture of Zagier which states that the constant term of the automorphic function $|Δ(x+iy)|^2$ i.e., the Lambert series $\sum_{n=1}^\infty τ(n)^2 e^{-4 πn y}$ can be expressed in terms of the non-trivial zeros of the Riemann zeta function. In this article, we study a certain Lambert series associated to Siegel cusp forms and observe a similar phenomenon.

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Babita, Abhash Kumar Jha, Abhishek Juyal, Bibekananda Maji. 2023-05-12. An asymptotic expansion for a Lambert series associated to Siegel cusp forms. https://arxiv.org/abs/2305.07412

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