Density of integers that are the sum of four cubes of primes in short intervals

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• 作者：H. Liu ; F. Zhao
• 关键词：Key words and phrasescircle method ; sieve method ; exponential sum over primes ; short interval
• 刊名：Acta Mathematica Hungarica
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：151
• 期：1
• 页码：8-23
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1588-2632
• 卷排序：151

文摘

Let \({\mathcal {L}}\) be the set of integers n which can be written as$$ n=p_1^3 + p_2^3+p_3^3+p_4^3. $$Using the circle method and sieves, we prove that \({\sum_{N < n \leq N+Y , {n\in \mathcal {L}}} 1\geq \gamma Y}\) holds for \({Y=N^{17/18}}\), where \({\gamma > 0}\) is an absolute constant.Key words and phrasescircle methodsieve methodexponential sum over primesshort intervalThis work is supported by Tianyuan Mathematics Foundation (Grant No. 11126325), National Natural Science Foundation of China (Grant No. 11371122, 11471112) and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (China).