切比雪夫函数$\vartheta$和$\psi$的更优估计
数论
2013-03-01 v1
摘要
本文利用H. Kadiri得到的新无零点区域以及Xavier Gourdon计算出的临界线上黎曼ζ函数的前个零点，给出了切比雪夫函数和的一些改进结果。证明中的方法类似于Rosser-Shoenfeld关于该主题的论文。
引用
@article{arxiv.1302.7208,
title = {Sharper estimates for Chebyshev's functions $\vartheta$ and $\psi$},
author = {Sadegh Nazardonyavi and Semyon Yakubovich},
journal= {arXiv preprint arXiv:1302.7208},
year = {2013}
}
备注
After finishing this article we realized that some of the theorems of this article was found by Pierre Dusart. In this article we give the proofs with more details. The proof essentially similar to those of Rosser and Shoenfeld papers in this area