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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Zeros of p-adic forms
by
Jahan Zahid
University of Oxford

Given a system of forms of degrees di over the p-adic numbers, we ask the question: how many variables n do we need in the system to be able to guarantee a non-trivial zero? Artin conjectured that we must have n > d12 + ...+ dr2.

This conjecture has been verified for the case of a single quadratic and single cubic form. However it was proved to be false for the case of quartic forms.

We shall discuss some recent work concerning quintic forms and a system of cubic and quadratic forms.

Date received: June 9, 2008

Copyright © 2008 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 Conferences Inc. Document # cawl-73.