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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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Bounds for the coefficients of powers of the Delta-function
by
Jeremy Rouse
University of Illinois, Urbana-Champaign

Let tk(n) be the nth coefficient of the kth power of Ramanujan's classical Delta function. Work of Deligne implies that |tk(n)| ≤ Ck n(12k-1)/2 for some constant Ck. We will show that the constant Ck tends to zero very rapidly. The proof will use the fact (noticed by Goldfeld, Hoffstein and Lieman) that symmetric square L-functions associated to newforms have no Siegel zeroes.

Date received: June 10, 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-76.