数域中素理想在算术级数中的平均分布

对于算术级数中的素数，我们有经典的Bombieri-Vinogradov定理与Barban–Davenport–Halberstam 定理。这两个定理在很多数论问题中都起着非常重要的作用。本项目主要在数域中研究素理想在算术级数中的平均分布问题。这属于解析数论与代数数论的交叉领域。我们将利用大筛法，圆法等解析工具研究Chebyshev密度定理中误差项的均值，对稀疏模情形建立相应的Bombieri-Vinogradov型定理与Barban-Davenport-Halberstam型定理。

For the distribution of primes in arithmetic progression，there are Bombieri-Vinogradov theorem and Barban–Davenport–Halberstam theorem. These two theorems play very important roles in many problems in number theory. In our project, we will study the average distribution of prime ideals in arithmetic progressions over number fields. This belongs to the area where analytic and algebraic number theory meet. We will use analytic tools, such as large sieve and circle method, to study the moments of the error term in Chebyshev density thorem and establish Bombieri-Vinogradov and Barban–Davenport–Halberstam type theorems for sparse sets of moduli.