Abstract
In 2000, Hafner and Stopple proved a conjecture of Zagier which states that the constant term of the automorphic function \(|\Delta (x+iy)|^2\), i.e., the Lambert series \(\sum _{n=1}^\infty \tau (n)^2 e^{-4 \pi n y}\), can be expressed in terms of the non-trivial zeros of the Riemann zeta function. In this article, we study an asymptotic expansion of a generalized version of the aforementioned Lambert series associated with Siegel cusp forms.
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The first author thanks IIT (BHU) Varanasi for financial support. The second author is partially supported by SERB Start-up Research Grant (File No. SRG/2022/000487) and MATRICS grant (File No. MTR/2022/000659). The last author’s research is supported by SERB MATRICS grant (File No. MTR/2022/000545) and CRG grant (File No. CRG/2023/002122). Both the authors thank SERB for the support.
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Babita, Jha, A.K., Juyal, A. et al. An asymptotic expansion for a Lambert series associated with Siegel cusp forms. Ramanujan J (2024). https://doi.org/10.1007/s11139-024-00864-z
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DOI: https://doi.org/10.1007/s11139-024-00864-z