Waring–Goldbach Problem of Even Powers in Short Intervals

Abstract

In this paper, we study the average behaviour of the representations of $n=p_1^2+p_2^4+p_3^4+p_4^k$ over short intervals for $k\ge 4$ , where $p_1,p_2,p_3,p_4$ are prime numbers. This improves the previous results.