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On a theorem of Ihara

Rastegar, A ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. Publisher: Sharif University of Technology , 2005
  3. Abstract:
  4. Let p be a prime number and let n be a positive integer prime to p. By an Ihara-result, one means the existence of an injection with torsion-free cokernel, from a full lattice, in the space of p-old modular forms, into a full lattice, in the space of all modular forms of level np. In this paper, Ihara-results are proven for genus two Siegel modular forms, Siegel-Jacobi forms and Hilbert modular forms. Ihara did the genus one case of elliptic modular forms [1]. A geometric formulation is proposed for the notion of p-old Siegel modular forms of genus two, using clarifying comments by R. Schmidt [2] and, then, following suggestions in an earlier paper [3] on how to prove Ihara results. The main theorem in [3] is used, where an argument by G. Pappas has been extended to prove the torsion-freeness of certain cokernel, using the density of Hecke-orbits in the moduli space of principally polarized abelian varieties and in the Hilbert-Blumenthal moduli space, which was proved by C. Chai [4]. © Sharif University of Technology
  5. Keywords:
  6. Elastic moduli ; Ellipsometry ; Integer programming ; Theorem proving ; Torsion testing ; Geometric formulation ; Positive integers ; Prime numbers ; Torsion-free cokernel ; Crystal lattices ; mathematical method ; Abelia
  7. Source: Scientia Iranica ; Volume 12, Issue 1 , 2005 , Pages 1-9 ; 10263098 (ISSN)
  8. URL: http://scientiairanica.sharif.edu/article_2463.html