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Exceptional sets in Waring's problem: two squares and $s$ biquadrates

Volume 162 / 2014

Lilu Zhao 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.

Authors

  • Lilu ZhaoSchool of Mathematics
    Hefei University of Technology
    Hefei 230009, People's Republic of China
    e-mail

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