Mean squares of quadratic twists of the Fourier coefficients of modular forms

Peng Gao; Yuetong Zhao

doi:10.1007/s11139-026-01420-7

Mean squares of quadratic twists of the Fourier coefficients of modular forms

Peng Gao^*
, Yuetong Zhao

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

In this paper, we evaluate asymptotically a smoothed version of the sum (Formula presented.) where 8d· is the Kronecker symbol, ∑∗ denotes a sum over positive odd square-free integers and λf(n) are Fourier coefficients of a given modular form f.

源语言	英语
文章编号	42
期刊	Ramanujan Journal
卷	70
期	3
DOI	https://doi.org/10.1007/s11139-026-01420-7
出版状态	已出版 - 7月 2026

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10.1007/s11139-026-01420-7

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title = "Mean squares of quadratic twists of the Fourier coefficients of modular forms",

abstract = "In this paper, we evaluate asymptotically a smoothed version of the sum (Formula presented.) where 8d· is the Kronecker symbol, ∑∗ denotes a sum over positive odd square-free integers and λf(n) are Fourier coefficients of a given modular form f.",

keywords = "Mean square, Modular L-functions, Quadratic Dirichlet character",

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AU - Gao, Peng

AU - Zhao, Yuetong

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

PY - 2026/7

Y1 - 2026/7

N2 - In this paper, we evaluate asymptotically a smoothed version of the sum (Formula presented.) where 8d· is the Kronecker symbol, ∑∗ denotes a sum over positive odd square-free integers and λf(n) are Fourier coefficients of a given modular form f.

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KW - Mean square

KW - Modular L-functions

KW - Quadratic Dirichlet character

UR - https://www.scopus.com/pages/publications/105041315650

U2 - 10.1007/s11139-026-01420-7

DO - 10.1007/s11139-026-01420-7

M3 - 文章

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SN - 1382-4090

VL - 70

JO - Ramanujan Journal

JF - Ramanujan Journal

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Mean squares of quadratic twists of the Fourier coefficients of modular forms

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