Exponential sums over primes in short intervals
Exponential sums over primes in short intervals
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DOI：
10.1016/j.jnt.2014.09.004
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发表时间：
2015-03
影响因子：
0.7
通讯作者：
Bingrong Huang;Zhiwei Wang
中科院分区：
文献类型：
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作者：
Bingrong Huang;Zhiwei Wang
设Λ (n)为von Mangoldt函数，x为实数，且2≤y≤x。本文改进了短区间内k (x, y; α)=∑x< n≤x+ y Λ (n) e （n k α）在k≥4时对所有α∈[0,1]的指数和的估计。然后结合Hardy-Littlewood方法，给出了可加素数理论中Hua定理的一些短区间变式。
Let Λ (n) be the von Mangoldt function, x real and 2≤ y≤ x. This paper improves the estimate on the exponential sum over primes in short intervals S k (x, y; α)=∑ x< n≤ x+ y Λ (n) e (n k α) when k≥ 4 for all α∈[0, 1]. And then combined with the Hardy–Littlewood method, this enables us to give some short interval variants of Hua's theorems in additive prime number theory.