Triple correlation sums of coefficients of cusp forms

被引：4

作者：

Hulse, Thomas A. ^{[1
]}

Kuan, Chan Ieong ^{[2
]}

Lowry-Duda, David ^{[3
]}

Walker, Alexander ^{[4
]}

机构：

[1] Boston Coll, Math Dept, Chestnut Hill, MA 02467 USA

[2] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China

[3] ICERM, 121 South Main St,Box E,11th Floor, Providence, RI 02903 USA

[4] Rutgers Univ Hill, Ctr Math Sci, Dept Math, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

来源：

JOURNAL OF NUMBER THEORY | 2021年 / 220卷

基金：

英国工程与自然科学研究理事会;

关键词：

Modular forms; Convolution sums; Multiple Dirichlet series; Spectral theory; FOURIER COEFFICIENTS; MOMENT;

D O I：

10.1016/j.jnt.2020.08.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We produce nontrivial asymptotic estimates for shifted sums of the form Sigma a(h)b(m)c(2m - h), in which a(n), b(n), c(n) are un-normalized Fourier coefficients of holomorphic cusp forms. These results are unconditional, but we demonstrate how to strengthen them under the Riemann Hypothesis. As an application, we show that there are infinitely manythree term arithmetic progressions n - h, n, n + h such that a(n - h)a(n)a(n + h) not equal 0. (c) 2020 Elsevier Inc. All rights reserved.

引用

页码：1 / 18

页数：18

共 19 条

[1] Shifted convolution sums and subconvexity bounds for automorphic L-functions
Blomer, V
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2004, 2004 (73) : 3905 - 3926
[2] The spectral decomposition of shifted convolution sums
Blomer, Valentin
Harcos, Gergely
[J]. DUKE MATHEMATICAL JOURNAL, 2008, 144 (02) : 321 - 339
[3] On triple correlations of divisor functions
Blomer, Valentin
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2017, 49 (01) : 10 - 22
[4] FUNCTIONAL EQUATIONS WITH MULTIPLE GAMMA FACTORS AND AVERAGE ORDER OF ARITHMETICAL FUNCTIONS
CHANDRASEKHARAN, K
NARASIMHA, R
[J]. ANNALS OF MATHEMATICS, 1962, 76 (01) : 93 - &
[5] Goldfeld Dorian, 2015, STUDIES ADV MATH, V99
[6] HEATHBROWN DR, 1979, P LOND MATH SOC, V38, P385
[7] Multiple Dirichlet series and shifted convolutions
Hoffstein, Jeff
Hulse, Thomas A.
Reznikov, Andre
[J]. JOURNAL OF NUMBER THEORY, 2016, 161 : 457 - 533
[8] The second moment of sums of coefficients of cusp forms
Hulse, Thomas A.
Kuan, Chan Ieong
Lowry-Duda, David
Walker, Alexander
[J]. JOURNAL OF NUMBER THEORY, 2017, 173 : 304 - 331
[9] Hulse Thomas A., 2018, 2 MOMENTS GEN GAUSS
[10] Ivic A, 2001, STUD SCI MATH HUNG, V37, P391

← 1 2 →