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Mean values of long
Dirichlet polynomials with divisor coefficients
Fatma Çiçek, Alia Hamieh and Nathan Ng |
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Vol. 19 (2025), No. 7, 1427–1462
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DOI: 10.2140/ant.2025.19.1427
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Abstract |
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We prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower-order terms and a power saving error term. This is derived from a more general theorem on mean values of long smoothed Dirichlet polynomials that was previously established by the second and third authors (Adv. Math. 410:B (2022)). We thus establish a stronger form of a conjecture of Conrey and Gonek (Duke Math. J. 107:3 (2001), Conjecture 4) in the case of divisor functions. |
Keywords
Dirichlet polynomials, mean value problems, moments of
Riemann zeta function, generalized divisor functions,
additive divisor sums
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Mathematical Subject Classification
Primary: 11M06, 11M26, 11M41
Secondary: 11N37, 11N75
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Milestones
Received: 21 September 2023
Revised: 30 April 2024
Accepted: 16 July 2024
Published: 3 June 2025
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Authors |
| Fatma Çiçek | |
| Department of Mathematics and
Statistics University of Northern British Columbia Prince George, BC Canada |
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| Alia Hamieh | |
| Department of Mathematics and
Statistics University of Northern British Columbia Prince George, BC Canada |
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| Nathan Ng | |
| Department of Mathematics and
Computer Science University of Lethbridge Lethbridge, AB Canada |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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