DDT Theorem over ideal in quadratic field
Zhishan Yang, Zongqi Yu · AIMS Mathematics · 2025
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.