区间上素数定理的显式均值估计

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of the Australian Mathematical Society Pub Date : 2023-09-19 DOI:10.1017/s1446788723000113

MICHAELA CULLY-HUGILL, ADRIAN W. DUDEK

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引用次数: 0

摘要

本文给出了区间内素数定理的Selberg中值估计的一个显式版本，假设Riemann假设[25]。给出了质数和哥德巴赫数的短区间结果的两个应用。在黎曼假设下，我们证明了存在一个素数 $(y,y+32\,277\log ^2 y]$ 至少有一半 $y\in [x,2x]$ 对所有人 $x\geq 2$ 至少有一个哥德巴赫数 $(x,x+9696 \log ^2 x]$ 对所有人 $x\geq 2$ ．

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AN EXPLICIT MEAN-VALUE ESTIMATE FOR THE PRIME NUMBER THEOREM IN INTERVALS

Abstract This paper gives an explicit version of Selberg’s mean-value estimate for the prime number theorem in intervals, assuming the Riemann hypothesis [25]. Two applications are given to short-interval results for primes and for Goldbach numbers. Under the Riemann hypothesis, we show there exists a prime in $(y,y+32\,277\log ^2 y]$ for at least half the $y\in [x,2x]$ for all $x\geq 2$ , and at least one Goldbach number in $(x,x+9696 \log ^2 x]$ for all $x\geq 2$ .

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来源期刊

Journal of the Australian Mathematical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The Journal of the Australian Mathematical Society is the oldest journal of the Society, and is well established in its coverage of all areas of pure mathematics and mathematical statistics. It seeks to publish original high-quality articles of moderate length that will attract wide interest. Papers are carefully reviewed, and those with good introductions explaining the meaning and value of the results are preferred. Published Bi-monthly Published for the Australian Mathematical Society