Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-26T08:55:28.095Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  01 May 2003

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]

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
Copyright
2003 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)