Computations of spaces of Siegel modular cusp forms

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概要

• 論文の詳細を見る

• Simple homomorphisms to elliptic modular forms are defined on the ring of Siegel modular forms and linear relations on the Fourier coefficients of Siegel modular forms are implied by the codomains of these homomorphisms. We use the linear relations provided by these homomorphisms to compute the Siegel cusp forms of degree n and weight k in some new cases: (n,k)=(4,14), (4,16), (5,8), (5,10), (6,8). We also compute enough Fourier coefficients using this method to determine the Hecke eigenforms in the nontrivial cases. We also put the open question of whether our technique always succeeds in a precise form. As a partial converse we prove that the Fourier series of Siegel modular forms are characterized among all formal series by the codomain spaces of these homomorphisms and a certain boundedness condition.

• 社団法人 日本数学会の論文
• 2007-01-01

著者

• Poor Cris

  Department Of Mathematics Fordham University

• YUEN David

  Department of Mathematics Lake Forest College

• Yuen David

  Department Of Geology And Geophysics And Minnesota Supercomputing Institute University Of Minnesota

• YUEN David

  Department of Geology and Geophysics and Minnesota Supercomputer Institute, University of Minnesota

関連論文

• COMPUTATIONS OF SPACES OF SIEGEL MODULAR CUSP FORMS (Automorphic Forms and their Dirichlet series)
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• COMPUTING SIEGEL MODULAR FORMS AND PARAMODULARITY (Automorphic forms, trace formulas and zeta functions)

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