Theory of the Siegel Modular
نویسنده
چکیده
In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties of the Siegel modular variety, (hypothetical) motives attached to Siegel modular forms and a cohomology of the Siegel modular variety. To the memory of my mother
منابع مشابه
On Atkin-Lehner correspondences on Siegel spaces
We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime l...
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In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties of the Siegel modular variety, (hypothetical) motives attached to Siegel modular forms and a cohomology of the Siegel modular variety. To the memory of my mother
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Siegel modular forms can be thought of as modular forms in more than one variable. Introduced in the 1930’s by Siegel in his analytic study of quadratic forms, they nowadays occur naturally in many unexpected places. We develop the basic theory from scratch, assuming only that the listener/reader has seen some rudiments of modular forms in one variable. We list some of the many applications and...
متن کاملAlmost holomorphic Poincaré series corresponding to products of harmonic Siegel–Maass forms
We investigate Poincaré series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincaré series are almost holomorphic as well. In general, this is not the c...
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تاریخ انتشار 2008