黎曼 zeta 函数高阶导数的一个离散中值定理
数论
2026-05-25 v3
摘要
我们证明，黎曼 zeta 函数的第 阶导数在对其非平凡零点求和时，对于 为奇数/偶数分别在中值意义下为实且正/负。我们通过给出这些求和的完全渐近展开式来证明这一点。
关键词
引用
@article{arxiv.2106.03005,
title = {A discrete mean-value theorem for the higher derivatives of the Riemann zeta function},
author = {Christopher Hughes and Andrew Pearce-Crump},
journal= {arXiv preprint arXiv:2106.03005},
year = {2026}
}
备注
This version adds a couple of improvements which were found after the paper was published (At the end of section 1, we state a better error term under RH and a neater way of presenting the main terms)