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ON WARING’S PROBLEM: TWO SQUARES AND THREE BIQUADRATES

Published online by Cambridge University Press:  28 June 2013

John B. Friedlander
Affiliation:
Department of Mathematics, University of Toronto, Toronto ON,Canada, M5S 2E4 email [email protected]
Trevor D. Wooley
Affiliation:
School of Mathematics, University of Bristol, University Walk, Clifton, Bristol BS8 1TW,U.K. email [email protected]
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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 $8\nmid n$, $n\not\equiv 2~(\text{mod} ~3)$ and $n\not\equiv 14~(\text{mod} ~16)$ are the sum of two squares and three biquadrates.

Type
Research Article
Copyright
Copyright © University College London 2013 

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