一类不等幂次的Waring-Goldbach问题的例外集  

The exceptional sets of a Waring-Goldbach problem with unequal powers

作　　者：朱豆豆 ZHU Doudou(College of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《西安工程大学学报》2021年第6期138-145,共8页Journal of Xi’an Polytechnic University

基　　金：国家自然科学基金(12071132)。

摘　　要：研究正奇数n=p_(1)+p^(3)_(2)+p^(k)_(3)(k∈N且k≥4)的可表问题。运用堆垒素数论中的圆法,借助圆法中的迭代方法处理主区间,并利用指数和方法处理余区间,得到以下结论:对于给定的充分大的正整数N和任意实数ε>0,除O(N31/60+2/k-2/3k×2^(k-1)+ε)个例外,所有的正奇数n(n≤N)都可以表示为p_(1)+p^(3)_(2)+p^(k)_(3),其中p_(1)、p_(2)、p_(3)为素数。The representability of positive odd number n=p_(1)+p^(3)_(2)+p^(k)_(3)(k∈N and k≥4)was studied.The circle method in additive number theory and the iterative method in the circle method were used to deal with the main arcs and the exponential sum method was used to deal with the minor arcs.The final conclusions were reached:Let N be a sufficiently large integer,then for anyε>0,it is proved that with at most O(N31/60+2/k-2/3k×2^(k-1)+ε)exceptions,all odd positive integers up to N can be represented in the form p_(1)+p^(3)_(2)+p^(k)_(3),where p_(1)、p_(2)、p_(3) are prime numbers.

关 键 词：圆法 奇异级数 例外集 主区间 余区间 

分 类 号：O156[理学—数学]