Email this article Nondiagonal terms in the second moment of automorphic $L$-functions
- Authors: Frolenkov D.A.1,2
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Affiliations:
- Pacific National University
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 211, No 8 (2020)
- Pages: 114-131
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133346
- DOI: https://doi.org/10.4213/sm9313
- ID: 133346
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Abstract
We investigate the exact formula for the second moment of central $L$-values associated to primitive cusp forms of level one and weight $k\to\infty$, $k\in\mathbb N$, which was proved by Kuznetsov in 1994. Nondiagonal terms in this formula are expressed in terms of several convolution sums of divisor functions. We investigate the main terms of the convolution sums and show that they cancel out.Bibliography: 8 titles.
About the authors
Dmitry Andreevich Frolenkov
Pacific National University; Steklov Mathematical Institute of Russian Academy of Sciences
Email: frolenkov@mi-ras.ru
Candidate of physico-mathematical sciences, no status
References
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