Exceptional sets in Waring's problem: two squares and $s$ biquadrates
Volume 162 / 2014
Acta Arithmetica 162 (2014), 369-379
MSC: Primary 11P05; Secondary 11P55, 11N37.
DOI: 10.4064/aa162-4-4
Abstract
Let $R_s(n)$ denote the number of representations of the positive number $n$ as the sum of two squares and $s$ biquadrates. When $s=3$ or $4$, it is established that the anticipated asymptotic formula for $R_s(n)$ holds for all $n\le X$ with at most $O(X^{(9-2s)/8+\varepsilon })$ exceptions.
