O. M. Fomenko, “Mean value theorems for automorphic $L$-functions”, Algebra i Analiz, 19:5 (2007), 246–264; St. Petersburg Math. J., 19:5 (2008), 853

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Algebra i Analiz, 2007, Volume 19, Issue 5, Pages 246–264 (Mi aa143)

This article is cited in 14 scientific papers (total in 14 papers)

Research Papers

Mean value theorems for automorphic

$L$ -functions

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Full-text PDF (206 kB) Citations (14)

References:

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Abstract: Let

$f$ be a holomorphic Hecke eigencuspform of even weight

$k\ge 12$ for

$\mathrm{SL}(2, \mathbb{Z})$ and let

$L(s,\mathrm{sym}^2f)$ be the symmetric square

$L$ -function of

$f$ . Let

$C(x)$ be the summatory function of the coefficients of

$L(s,\mathrm{sym}^2 f)$ . The true order is found for

$\int_0^x C(y)^2\,dy.$

Keywords: Symmetric square

$L$ -function, summatory function, Euler product, Voronoi formula, mean value.

Received: 05.04.2007

English version:
St. Petersburg Mathematical Journal, 2008, Volume 19, Issue 5, Pages 853–866
DOI: https://doi.org/10.1090/S1061-0022-08-01024-8

Bibliographic databases:

Document Type: Article

MSC: 11M41

Language: Russian

Citation: O. M. Fomenko, “Mean value theorems for automorphic

$L$ -functions”, Algebra i Analiz, 19:5 (2007), 246–264; St. Petersburg Math. J., 19:5 (2008), 853–866

Citation in format AMSBIB

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\jour St. Petersburg Math. J.

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\vol 19

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\pages 853--866

\crossref{https://doi.org/10.1090/S1061-0022-08-01024-8}

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Linking options:

https://www.mathnet.ru/eng/aa143

https://www.mathnet.ru/eng/aa/v19/i5/p246

This publication is cited in the following 14 articles:

Huafeng Liu, Xiaojie Yang, “The Average Behaviors of the Fourier Coefficients of j-th Symmetric Power L-Function over Two Sparse Sequences of Positive Integers”, Bull. Iran. Math. Soc., 50:1 (2024)
Weili Yao, “Fourier coefficients of cusp forms on special sequences”, Int. J. Number Theory, 20:04 (2024), 1125
Huafeng Liu, “The Average Behavior of Fourier Coefficients of Symmetric Power L-Functions”, Bull. Malays. Math. Sci. Soc., 46:6 (2023)
Guodong Hua, Bin Chen, Lijing Pan, Xiaofang Chen, “On higher moments of Dirichlet coefficients attached to symmetric square L-functions over certain sparse sequence”, Rend. Circ. Mat. Palermo, II. Ser, 72:8 (2023), 4195
Guodong Hua, “The average behaviour of a hybrid arithmetic function associated to cusp form coefficients over certain sparse sequence”, Filomat, 37:23 (2023), 7791
Guodong Hua, “Discrete mean square of the coefficients of triple product L-functions over certain sparse sequence”, Bulletin des Sciences Mathématiques, 180 (2022), 103194
Guodong Hua, “The average behaviour of Hecke eigenvalues over certain sparse sequence of positive integers”, Res. number theory, 8:4 (2022)
Luo Sh., Lao H., Zou A., “Asymptotics For the Dirichlet Coefficients of Symmetric Power l-Functions”, Acta Arith., 199:3 (2021), 253–268
He X., “Integral Power Sums of Fourier Coefficients of Symmetric Square l-Functions”, Proc. Amer. Math. Soc., 147:7 (2019), 2847–2856
O. M. Fomenko, “On the mean square of the error term for Dedekind zeta functions”, J. Math. Sci. (N. Y.), 217:1 (2016), 125–137
Lao H., “On the fourth moment of coefficients of symmetric square L-function”, Chin. Ann. Math. Ser. B, 33:6 (2012), 877–888
O. M. Fomenko, “On summatory functions for automorphic $L$-functions”, J. Math. Sci. (N. Y.), 184:6 (2012), 776–785
Lao Huixue, “Mean square estimates for coefficients of symmetric power $L$-functions”, Acta Appl. Math., 110:3 (2010), 1127–1136
O. M. Fomenko, “Mean value theorems for a class of Dirichlet series”, J. Math. Sci. (N. Y.), 157:4 (2009), 659–673

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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