Abstract
Suppose that \(\mathbb {H}^*\) is the set of all primitive cusp forms f of even integral weight \(k\ge 2\) for the full modular group \(SL_2(\mathbb {Z})\). In this paper, we establish asymptotic formulas for the second moment of Fourier coefficients of the triple product L-function \(L(s, f\otimes f \otimes f)\) and the related L-function \(L(s, \textrm{sym}^2f \otimes f)\) attached to f on average, which improves previous results.
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Acknowledgements
The author is very grateful to the referee for many valuable suggestions and comments. This work is supported by the National Natural Science Foundation of China (Grant Nos 12171286 and 11801328).
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Liu, H. The second moment of the Fourier coefficients of triple product \({\varvec{L}}\)-functions. Proc Math Sci 133, 8 (2023). https://doi.org/10.1007/s12044-023-00733-7
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DOI: https://doi.org/10.1007/s12044-023-00733-7