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On Some Metaplectic Eisenstein Series
Journal of Mathematical Sciences, 2002The author uses methods developed by N. V. Proskurin to study a certain class of metaplectic Eisenstein series on a suitable subgroup of \(\text{Sp}_4 (\mathbb{Z}[\omega])\) where \(\omega= e^{2\pi i/3}\). Whereas Proskurin studied those Eisenstein series that are either associated with a minimal parabolic subgroup or with a metaplectic theta function ...
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Eisenstein Series and Partition Functions
Mathematical Methods in the Applied SciencesABSTRACTIn this work, using quotients of Dedekind eta functions of weight , we express certain Eisenstein series associated with congruence subgroups , of arbitrary weight. We then obtain new Ramanujan type identities on partition functions associated with certain eta quotients.
Sofiane Abdelhamid Atmani +2 more
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1973
Let ω1,ω2 be two complex numbers, different from zero, such that the quotient t =ω2/ω1 is not real. The totality Ω of all complex numbers m1ω1 + m2ω2 with m1m2 integers, forms a point-lattice in the complex plane.
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Let ω1,ω2 be two complex numbers, different from zero, such that the quotient t =ω2/ω1 is not real. The totality Ω of all complex numbers m1ω1 + m2ω2 with m1m2 integers, forms a point-lattice in the complex plane.
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Eisenstein Series on Shimura Varieties
The Annals of Mathematics, 1984In a previous paper [Invent. Math. 63, 305--310 (1981; Zbl 0452.10031)] the author proved rationality properties of the Fourier coefficients of holomorphic Eisenstein series attached to cusp forms on boundary components of Siegel's upper half plane of degree \(n\). The proof -- which did not use any explicit knowledge of the Fourier coefficients -- was
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2005
In Chap. 5, we already saw the Epstein zeta function, actually two zeta functions, one primitive and the other one completed by a Riemann zeta function. Indeed, let Y ∈ Posn.
Jay Jorgenson, Serge Lang
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In Chap. 5, we already saw the Epstein zeta function, actually two zeta functions, one primitive and the other one completed by a Riemann zeta function. Indeed, let Y ∈ Posn.
Jay Jorgenson, Serge Lang
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2005
In this chapter, we start systematically to investigate what happens when we take the trace over the discrete groups γ = GLn(Z), for various objects. In the first section, we describe a universal adjointness relation which has many applications. One of them will be to the Fourier expansion of the Eisenstein series.
Jay Jorgenson, Serge Lang
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In this chapter, we start systematically to investigate what happens when we take the trace over the discrete groups γ = GLn(Z), for various objects. In the first section, we describe a universal adjointness relation which has many applications. One of them will be to the Fourier expansion of the Eisenstein series.
Jay Jorgenson, Serge Lang
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Iterated Eisenstein ��-integrals and Multiple Eisenstein L-series
2019In this paper we study iterated Eisenstein -integrals and multiple Eisenstein L-series, they are functions on the complex upper half plane and form two Q-algebras. They reduce to iterated Eisenstein integrals and multiple Hecke L-functions with respect to Eisenstein series respectively after analytic extension when ->0.
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Diagonalizing Eisenstein Series. I
1990In this paper we consider the action of Hecke operators T n (n ∈ IN), and their adjoint operators T* n , on Eisenstein series belonging to the group Γ0(N) and having integral weight k > 2 and arbitrary character χ modulo N. It is shown that the space ɛ k (x) spanned by these Eisenstein series splits up into a number of subspaces ɛ k (x,t)> where t is a
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