DDT Theorem over ideal in quadratic field

Zhishan Yang; Zongqi Yu; Zhishan Yang; Zongqi Yu

doi:10.3934/math.2025089

AIMS Mathematics

2025, Volume 10, Issue 1: 1921-1934. doi: 10.3934/math.2025089

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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

Received: 31 October 2024 Revised: 30 December 2024 Accepted: 14 January 2025 Published: 05 February 2025
MSC : 11M06, 111N99, 11R04

Let $ K $ be a quadratic field and $ \mathfrak{a} $ be a fixed integral ideal of $ O_K $. In this paper, we investigate the distribution of ideals that divide $ \mathfrak{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.
- Selberg-Delange method,
- the distribution,
- quadratic field,
- the arcsine distribution
Citation: Zhishan Yang, Zongqi Yu. DDT Theorem over ideal in quadratic field[J]. AIMS Mathematics, 2025, 10(1): 1921-1934. doi: 10.3934/math.2025089

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Abstract

Let $ K $ be a quadratic field and $ \mathfrak{a} $ be a fixed integral ideal of $ O_K $. In this paper, we investigate the distribution of ideals that divide $ \mathfrak{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.

References

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