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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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Asymptotic Lower Bounds for Diophantine Inequalities
by
Eric Freeman
University of Colorado

It is shown that there is a finite bound s0(k) such that certain diagonal Diophantine equalities of degree k in s >= s0(k) variables must have >> Ps-k integral solutions x in the box |x| <= P, for sufficiently large real numbers P. The result relates to work of Davenport and Heilbronn, who were able to demonstrate this only for a sequence of P tending to infinity.

Date received: March 14, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cadx-96.