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Research Article | Open Access

A prime number theorem in short intervals for dihedral Maass newforms

Data Science Institute, Shandong University, No. 27 Shanda South Road, Jinan 250100, China
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Abstract

In this paper, we prove a prime number theorem in short intervals for the Rankin-Selberg L-function L ( s , ϕ × ϕ ), where ϕ is a fixed dihedral Maass newform. As an application, we give a lower bound for the proportion of primes in a short interval at which the Hecke eigenvalues of the dihedral form are greater than a given constant.

Keywords

prime number theoremHecke eigenvalueRankin-Selberg L-functionzero-free regionzero density estimate
CLC number: 11F30, 11N05

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 4896-4906
DOI: 10.3934/math.2024238

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Cite this article:
Guan B. A prime number theorem in short intervals for dihedral Maass newforms. AIMS Mathematics, 2024, 9(2): 4896-4906. https://doi.org/10.3934/math.2024238

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Received: 17 November 2023
Revised: 12 January 2024
Accepted: 18 January 2024
Published: 15 February 2024
©2024 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)