Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

An asymptotic expansion for a Lambert series associated to the symmetric square $L$-function (2105.07130v1)

Published 15 May 2021 in math.NT

Abstract: 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 non-trivial zeros of the Riemann zeta function $\zeta(s)$. Later, Chakraborty, Kanemitsu and the second author extended this phenomenon for any Hecke eigenform over the full modular group. In this paper, we study an asymptotic expansion of the Lambert series \begin{equation*} yk \sum_{n=1}\infty \lambda_{f}( n2 ) \exp (- ny), \quad \textrm{as}\,\, y \rightarrow 0{+}, \end{equation*} where $\lambda_f(n)$ is the $n$th Fourier coefficient of a Hecke eigen form $f(z)$ of weight $k$ over the full modular group.

Summary

We haven't generated a summary for this paper yet.