关于短区间素数定理中的误差
数论
2025-10-30 v3
摘要
在假设黎曼假设的前提下，我们使用平滑论证推导了素数定理和 Mertens 定理在短区间类比中误差项的显式界。我们的结果在常数项和适用范围上均改进了先前的界，特别是改进并扩展了 Cully-Hugill 和 Dudek 的早期工作。
引用
@article{arxiv.2403.11814,
title = {On the error in the prime number theorem in short intervals},
author = {Ethan Simpson Lee},
journal= {arXiv preprint arXiv:2403.11814},
year = {2025}
}
备注
Major updates to the presentation of the paper and the smoothing argument. The main results of this paper are improved, and the arguments are cleaner. As usual: 15 pages, comments and suggestions are warmly welcomed!