Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions

Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions

In this paper, we study two-dimensional divisor problems of the Fourier coefficients of some automorphic product <i>L</i>-functions attached to the primitive holomorphic cusp form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline&quo...

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Main Authors: Jing Huang, Huafeng Liu, Fuxia Xu
Format: Article
Language:English
Published: MDPI AG 2021-02-01
Series:Symmetry
Subjects:
Hecke L-function
symmetric L-function
divisor problem
Fourier coefficients
Online Access:https://www.mdpi.com/2073-8994/13/2/359
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spelling doaj-1d2e7477be5d40e6b77fe2bdc342c6892021-02-23T00:03:52ZengMDPI AGSymmetry2073-89942021-02-011335935910.3390/sym13020359Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-FunctionsJing Huang0Huafeng Liu1Fuxia Xu2School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong 250358, ChinaIn this paper, we study two-dimensional divisor problems of the Fourier coefficients of some automorphic product <i>L</i>-functions attached to the primitive holomorphic cusp form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> with weight <i>k</i> for the full modular group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>L</mi><mn>2</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">Z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Additionally, we establish the upper bound and the asymptotic formula for these divisor problems on average, respectively.https://www.mdpi.com/2073-8994/13/2/359Hecke L-functionsymmetric L-functiondivisor problemFourier coefficients
collection DOAJ
language English
format Article
sources DOAJ
author Jing Huang
Huafeng Liu
Fuxia Xu
spellingShingle Jing Huang
Huafeng Liu
Fuxia Xu
Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions
Symmetry
Hecke L-function
symmetric L-function
divisor problem
Fourier coefficients
author_facet Jing Huang
Huafeng Liu
Fuxia Xu
author_sort Jing Huang
title Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions
title_short Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions
title_full Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions
title_fullStr Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions
title_full_unstemmed Two-Dimensional Divisor Problems Related to Symmetric <i>L</i>-Functions
title_sort two-dimensional divisor problems related to symmetric <i>l</i>-functions
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-02-01
description In this paper, we study two-dimensional divisor problems of the Fourier coefficients of some automorphic product <i>L</i>-functions attached to the primitive holomorphic cusp form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> with weight <i>k</i> for the full modular group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>L</mi><mn>2</mn></msub><mrow><mo>(</mo><mi mathvariant="double-struck">Z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Additionally, we establish the upper bound and the asymptotic formula for these divisor problems on average, respectively.
topic Hecke L-function
symmetric L-function
divisor problem
Fourier coefficients
url https://www.mdpi.com/2073-8994/13/2/359
work_keys_str_mv AT jinghuang twodimensionaldivisorproblemsrelatedtosymmetricilifunctions
AT huafengliu twodimensionaldivisorproblemsrelatedtosymmetricilifunctions
AT fuxiaxu twodimensionaldivisorproblemsrelatedtosymmetricilifunctions
_version_ 1724255342848638976

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