An asymptotic expansion for a Lambert series associated to Siegel cusp forms of degree $n$
| Autor: | Babita, Jha, Abhash Kumar, Maji, Bibekananda, Pal, Manidipa |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 15 pages, comments are welcome! arXiv admin note: text overlap with arXiv:2305.07412 |
| Databáze: | arXiv |
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