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Siegel modular form
About: Siegel modular form is a research topic. Over the lifetime, 1271 publications have been published within this topic receiving 22197 citations.
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Book•
01 Jan 1971
TL;DR: The cohomology group assoicated with cusp forms and arithmetic Fuschian groups of the first kind was introduced in this paper..., where we have shown that it is possible to construct an algebraic algebraic curve and a complex multiplication of elliptic curves.
Abstract: * uschian groups of the first kind * Automorphic forms and functions * Hecke operators and the zeta-functions associated with modular forms * Elliptic curves * Abelian extensions of imaginary quadratic fields and complex multiplication of elliptic curves * Modular functions of higher level * Zeta-functions of algebraic curves and abelian varieties * The cohomology group assoicated with cusp forms * Arithmetic Fuschian groups
1,146 citations
Book•
01 Nov 2008
TL;DR: Modular forms, elliptic curves, and modular curves as Riemann surfaces have been used to define the Eichler-Shimura Relation and L-functions.
Abstract: Modular Forms, Elliptic Curves, and Modular Curves.- Modular Curves as Riemann Surfaces.- Dimension Formulas.- Eisenstein Series.- Hecke Operators.- Jacobians and Abelian Varieties.- Modular Curves as Algebraic Curves.- The Eichler-Shimura Relation and L-functions.- Galois Representations.
853 citations
Book•
01 Jan 1977
TL;DR: In this article, the authors present a general characterization of modular forms, including groups of matrices and bilinear mappings, groups of level 2 and sums of squares, hecke operators and congruence groups.
Abstract: 1. Groups of matrices and bilinear mappings 2. Mapping properties 3. Automorphic factors and multiplier systems 4. General properties of modular forms 5. Construction of modular forms 6. Functions belonging to the full modular group 7. Groups of level 2 and sums of squares 8. Modular forms of level N 9. Hecke operators and congruence groups 10. Applications.
417 citations
361 citations
307 citations