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Research Article | Open Access

Triple correlation sums of coefficients of θ-series

Fei Hou1( ), Bin Chen2
Department of Mathematics, College of Science, Xi'an University of Technology, Xi'an 710054, China
Department of Mathematics, College of Mathematics and Physics, Weinan Normal University, Weinan 714099, China
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Abstract

We investigate the triple correlation sums of coefficients of θ-series and prove an asymptotic formula with power-saving error term. As a result, we present that this type of sum is non-trivial in the regime H ≥ X 2 / 3 + ε .

Keywords

Jacobi theta seriesFourier coefficientstriple correlation sumsasymptotic formula
CLC number: 11F03, 11F30

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 25275-25287
DOI: 10.3934/math.20231289

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Hou F, Chen B. Triple correlation sums of coefficients of θ-series. AIMS Mathematics, 2023, 8(10): 25275-25287. https://doi.org/10.3934/math.20231289

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Received: 20 June 2023
Revised: 28 July 2023
Accepted: 17 August 2023
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)