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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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Finding the Slopes
by
Fernando Q. Gouvêa
Colby College

The theory of p-adic modular forms has taught us the importance of the slope (i.e., the p-adic valuation of the eigenvalue of the p-th Hecke operator) of a modular form. Very little, however, is known about what these slopes are. We will present some very surprising computational evidence and discuss what it might be telling us.

Date received: March 2, 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 Conferences Inc. Document # cadx-44.