Exceptional Set for Sums of Symmetric Mixed Powers of Primes

Author:

Li JinjiangORCID,Liu Chao,Zhang Zhuo,Zhang Min

Abstract

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.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference28 articles.

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4. Representation of an odd number as a sum of three primes;Vinogradov;Dokl. Akad. Nauk SSSR,1937

5. Some theorems concerning the theory of primes;Vinogradov;Mat. Sb.,1937

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