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The Bergé–Martinet Constant and Slopes of Siegel Cusp Forms
Author(s) -
Poor Cris,
Yuen David S.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306019138
Subject(s) - mathematics , cusp (singularity) , upper and lower bounds , hermite polynomials , constant (computer programming) , combinatorics , pure mathematics , modular form , cusp form , mathematical analysis , geometry , computer science , programming language
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 ⩽ 8. In degrees n = 5, 6 and 7 we settle the value of the generalized Hermite constantγ n ′introduced by Bergé and Martinet and find all dual‐critical pairs. 2000 Mathematics Subject Classification 11H55 (11F46).