论文标题
pnt的明确均值估计值
An explicit mean-value estimate for the PNT in intervals
论文作者
论文摘要
本文为塞尔伯格（Selberg）1943年的均值估算值提供了明确的版本，该估算值是根据Riemann假设的间隔定理的。给出了两个应用程序：短时间间隔的素数，以及短时间间隔的Goldbach数字（2个总和）。根据Riemann的假设，我们表明在$（y，y+32277 \ 32277 \ log^2 y] $中，至少$ y \ in [x，2x] $ in [x，2x] $ in [x，2x] $ in [x，2x] $ in $ x \ geq 2 $，以及至少一个goldbach in $（x，x，x，x+9696 \ log^2 x] $ x $ x $ x $ x $ x \ geq的$（x，x+9696 \ log^2 x] $。
This paper gives an explicit version of Selberg's 1943 mean-value estimate for the prime number theorem in intervals under the Riemann hypothesis. Two applications are given: for primes in short intervals, and Goldbach numbers (sums of two primes) in short intervals. Under the Riemann hypothesis, we show there exists a prime in $(y,y+32277\log^2 y]$ 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 $x\geq 2$.
