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THE BERGÉ–MARTINET CONSTANT AND SLOPES OF SIEGEL CUSP FORMS

Published online by Cambridge University Press:  19 December 2006

CRIS POOR  and
DAVID S. YUEN
CRIS POOR
Affiliation:
Department of Mathematics, Fordham University, Bronx, NY 10458, [email protected]
DAVID S. YUEN
Affiliation:
Department of Mathematics and Computer Science, Lake Forest College, 555 N. Sheridan Rd., Lake Forest, IL 60045, [email protected]
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Abstract

We give a theoretical lower bound for the slope of a Siegel modular cusp form that is as least as good as Eichler's lower bound. In degrees $n=5,6$ and 7 we show that our new bound is strictly better. In the process we find the forms of smallest dyadic trace on the perfect core for ranks $n \le 8$. In degrees $n=5,6$ and 7 we settle the value of the generalized Hermite constant $\gamma_n'$ introduced by Bergé and Martinet and find all dual-critical pairs.

Keywords

11H55 (11F46)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 913 - 924
Copyright
The London Mathematical Society 2006

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