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Slim exceptional sets and the asymptotic formula in Waring’s problem

Published online by Cambridge University Press:  01 May 2003

TREVOR D. WOOLEY
TREVOR D. WOOLEY
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, Michigan 48109-1109, U.S.A. e-mail: [email protected]
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Abstract

By avoiding a conventional application of Bessel’s inequality in favour of explicitly controlling an exponential sum over the exceptional set, in our previous work [9, 10], we have exploited additional variables so as to enhance exceptional set estimates in various additive problems of Waring type. In this paper we turn to the problem of establishing the expected asymptotic formula in Waring’s problem. The methods introduced herein, although discussed in the context of the asymptotic formula, should nonetheless provide a useful model for future excursions involving exceptional sets in additive problems.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 134 , Issue 2 , March 2003 , pp. 193 - 206
Copyright
2003 Cambridge Philosophical Society

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