On Waring's problem: two squares and three biquadrates

Abstract

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing n, n not congruent to 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2 squares and 3 biquadrates.

to appear in Mathematika

Cited by in corpus (3)

• On Waring's problem: some consequences of Golubeva's method
• On Waring's problem: two squares, two cubes and two sixth powers
• Exceptional sets in Waring's problem: two squares and s biquadrates