定义在素数上的函数的一些积分的新估计

Pub Date : 2022-01-01 DOI:10.7169/facm/2049

Christian Axler

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引用次数: 1

摘要

本文给出了包含素数上定义的算术函数的积分的新估计。这里的重点是质数计数函数$\pi(x)$和Chebyshev $\vartheta$函数。其中一些估计依赖于黎曼ζ函数$\zeta(s)$的非平凡零点上黎曼假设的正确性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New estimates for some integrals of functions defined over primes

In this paper we give new estimates for integrals involving some arithmetic functions defined over prime numbers. The main focus here is on the prime counting function $\pi(x)$ and the Chebyshev $\vartheta$-function. Some of these estimates depend on the correctness of the Riemann hypothesis on the nontrivial zeros of the Riemann zeta function $\zeta(s)$.

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