一类华林-哥德巴赫方程的小素数解问题  

Small solution of a Waring-Goldbach type equation

作　　者：高改芸 刘志新 GAO Gaiyun;LIU Zhixin(Department of Basic Education,Tianjin College,University of Science and Technology Beijing,Tianjin 301830,China;School of Mathematics,Tianjin University,Tianjin 300350,China)

机构地区：[1]北京科技大学天津学院基础部,天津301830 [2]天津大学数学学院,天津300350

出　　处：《纯粹数学与应用数学》2024年第3期450-464,共15页Pure and Applied Mathematics

基　　金：国家自然科学基金(11871367);天津市自然科学基金(19JCQNJC14200);第六批校级本科教育教学改革与研究项目(tyjy2021012).

摘　　要：华林-哥德巴赫方程的小素数解问题是堆垒素数论研究领域的重要研究课题,历来备受解析数论学者关注.本文研究一类满足必要条件的不等次幂华林-哥德巴赫方程的小素数解问题.利用标准的Hardy-Littlewood圆法和先进的Davenport方法,结合素变数三角和估计的最新成果及更加有效的Hölder不等式,得到该方程小素数解的更好上界,改进已有的研究结果.The problem of small prime solutions to theWaring-Goldbach type equation is an important research project in the field of additive prime number theory.It has attracted the attention of many analytic number theorists.This topic is to study the problem of small prime solutions to an unlike Waring-Goldbach type equation satisfying some necessary conditions.Using the standard Hardy-Littlewood cicle method and the advanced Davenport method,combining the latest results of the estimate of the exponential sum over primes and the more efficient Hölder inequalities,then it gets the better upper bound of small prime solutions to this equation and finally the result gives an improvement of the recent result.

关 键 词：华林-哥德巴赫问题 素数 Baker常数 Davenport方法 

分 类 号：O156.4[理学—数学]