几个堆垒素数问题定量研究

项目名称： 几个堆垒素数问题定量研究

项目编号： No.11471112

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 王天泽

作者单位： 华北水利水电大学

项目金额： 60万元

中文摘要： 本项目主要围绕下述三类堆垒数论问题开展定量研究：（1）借鉴Helfgott近期完全移除三素数定理中充分大条件，从而完整解决奇数Goldbach猜想的思想，寻求移除一些非线性低方幂素变数方程可解性对于充分大条件的依赖，比如移除华罗庚先生五平方素数定理中的充分大条件等。（2）结合近期算术组合和零点分布的有关研究及进展，继续研究Dirichlet L函数零点分布和密度估计的定量估计，进而考虑Linnik-Gallagher型方程最小素数解的定量上界估计，并继续考虑Baker关于素变数方程解的定量上界估计。（3）结合张益唐对孪生素数猜想的重大推进及Maynard等人的相关跟进，考虑有关均值定理的推广改进和应用，进而通过细化Maynard对Goldston-Pints-Yildirim型筛法的推广，探讨某些相关定量结果的直接改进和有关延伸。

中文关键词： 零点分布；素数论；指数和估计；圆法；筛法

英文摘要： The purpose of this project is to give some quantitative studies related to the following three kinds of problems in the field of additive prime number theory. (1)Consider to remove the sufficiently largecondition in the results of expressing integers as sums of lower prime powers,such as that in the classical theorem of professor Hua that every sufficiently large integer congruent to 5 modulo 24 is a sum of five prime squares.The investigation of these kinds of problems is interesting and valuable if one notes and compares it with a recent important result of Helfgott,which gave a complete solution to the classical odd Goldbach conjecture. (2)Using the latest numerical results in the field of arithmetic combinatorics and zeros of Dirichlet L functions, we continue to consider the numerical upper bound of the least prime solution of some Linnik-Gallagher equations, and consider the improvement of Baker's constant on the upper bound of solution of some equations with prime variables. (3)By some delicate investigation of the ideas and the methods of Yitang Zhang and James Maynard,we manage to discuss some related new kinds of mean value theorems,and then by considering the sieve of Goldston-Pints-Yildirim, we come to give some new quantitative results on the related problems,such as the prime twin conjecture itself.

英文关键词： distribution of zeros;prime number theory;estimates for exponential sum;circle method;sieve method