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Non-vanishing of the symmetric square L-function at the central point
by
Rizwan Khan
University of California, Los Angeles
We show that for a positive proportion of level 1 Hecke eigenforms of weight bounded by a large enough constant, the associated symmetric square L-function does not vanish at the central real point of its critical strip. When counting `harmonically' we optimize this proportion and observe that it agrees with proportions of non-vanishing found by other authors for other symplectic families of L-functions. Our harmonic proportion is just over 70%.
Date received: January 24, 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-04.