Slopes of integral lattices |
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Authors: | Cris Poor David S Yuen |
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Institution: | Department of Mathematics, Fordham University, Bronx, NY 10458, USA |
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Abstract: | We use the dyadic trace to define the concept of slope for integral lattices. We present an introduction to the theory of the slope invariant. The main theorem states that a Siegel modular cusp form f of slope strictly less than the slope of an integral lattice with Gram matrix s satisfies f(sτ)=0 for all τ in the upper half plane. We compute the dyadic trace and the slope of each root lattice and we give applications to Siegel modular cusp forms. |
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Keywords: | 11F46 (11H55) |
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