Exceptional Set for Sums of Symmetric Mixed Powers of Primes

Symmetry

Jinjiang Li¹  Chao Liu¹  Zhuo Zhang¹  Min Zhang² 

[1] Department of Mathematics, China University of Mining and Technology, Beijing 100083, China;School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China;

关键词: waring–goldbach problem;    circle method;    exceptional set;    symmetric form;   

DOI  :  10.3390/sym12030367

来源: DOAJ

【 摘 要 】

The main purpose of this paper is to use the Hardy−Littlewood method to study the solvability of mixed powers of primes. To be specific, we consider the even integers represented as the sum of one prime, one square of prime, one cube of prime, and one biquadrate of prime. However, this representation can not be realized for all even integers. In this paper, we establish the exceptional set of this kind of representation and give an upper bound estimate.

【 授权许可】

Unknown