Affiliation: University of Wisconsin
Email: rouse@math.wisc.edu
Title Of Talk: Vanishing and Non-Vanishing of Traces of Hecke Operators
URL: http://www.math.wisc.edu/~rouse/cv/trace.pdf
Abstract: Using a reformulation of the Eichler-Selberg trace formula, due to Frechette, Ono, and Papanikolas, we consider the problem of the vanishing (resp. non-vanishing) of traces of Hecke operators on spaces of even weight cusp forms with trivial Nebentypus character. For example, we show that for a fixed operator and weight, the set of levels for which the trace vanishes is effectively computable. Also, for a fixed operator the set of weight for which the trace vanishes (for any level) is finite. These results motivate the ``generalized Lehmer conjecture,'' that the trace does not vanish for even weights 2k >= 16 or 2k = 12.
Last update made Mon Nov 15 13:02:05 EST 2004.
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