WARING-GOLDBACH PROBLEM TWO SQUARES AND THREE BIQUADRATES

Let R(n) denote the number of representations of the positive integer n as the sum of two squares and three biquadrates of primes and we write epsilon(N) for the number of positive integers n satisfying n <= N, n 5, 53, 101 (mod 120) and vertical bar R(n) - Gamma(2)(1/2)Gamma(3)(1/4)/Gamma(7/4) e(n)n(3/4)/log(5) n vertical bar >= n(3/4)/log(11/2)n, where 0 < e(n) << 1 is the singular series. In this paper, we prove epsilon (N) << N15/32+epsilon for any epsilon > 0. This result constitutes a refinement upon that of Friedlander and Wooley (2014).