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Research Article | Open Access

DDT Theorem over ideal in quadratic field

Zhishan Yang, Zongqi Yu( )
School of Mathematics and Statistics, Qingdao University, 308 Ningxia Road, Shinan District, Qingdao, Shandong, China
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Abstract

Let K be a quadratic field and a be a fixed integral ideal of O K . In this paper, we investigate the distribution of ideals that divide a using the Selberg-Delange method. This is a natural variation of a result studied by Deshouillers, Dress, and Tenenbaum (often referred to as the DDT Theorem), and we find that this distribution converges to the arcsine distribution.

Keywords

Selberg-Delange methodthe distributionquadratic fieldthe arcsine distribution
CLC number: 11M06, 111N99, 11R04

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 1921-1934
DOI: 10.3934/math.2025089

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Cite this article:
Yang Z, Yu Z. DDT Theorem over ideal in quadratic field. AIMS Mathematics, 2025, 10(1): 1921-1934. https://doi.org/10.3934/math.2025089

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Received: 31 October 2024
Revised: 30 December 2024
Accepted: 14 January 2025
Published: 15 January 2025
©2025 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)