On the appearance of Eisenstein series through degeneration
نویسنده
چکیده
Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane H, and let M = Γ\H be the associated finite volume hyperbolic Riemann surface. If γ is parabolic, there is an associated (parabolic) Eisenstein series, which, by now, is a classical part of mathematical literature. If γ is hyperbolic, then, following ideas due to Kudla-Millson, there is a corresponding hyperbolic Eisenstein series. In this article, we study the limiting behavior of parabolic and hyperbolic Eisenstein series on a degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. If γ ∈ Γ corresponds to a degenerating hyperbolic element, then a multiple of the associated hyperbolic Eisenstein series converges to parabolic Eisenstein series on the limit surface.
منابع مشابه
Theta functions on covers of symplectic groups
We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. This representation is obtained from the residues of Eisenstein series on this group. If $r$ is odd, $nle r
متن کاملEEH: AGGH-like public key cryptosystem over the eisenstein integers using polynomial representations
GGH class of public-key cryptosystems relies on computational problems based on the closest vector problem (CVP) in lattices for their security. The subject of lattice based cryptography is very active and there have recently been new ideas that revolutionized the field. We present EEH, a GGH-Like public key cryptosystem based on the Eisenstein integers Z [ζ3] where ζ3 is a primitive...
متن کاملAND GENERATING FUNCTIONS FOR ARITHMETIC CYCLES by Stephen
The classical formula of Siegel and Weil identifies the values of Siegel–Eisenstein series at certain critical points as integrals of theta functions. When the critical point is the center of symmetry for the functional equation, the Fourier coefficients of the values of the ‘even’ Siegel–Eisenstein series thus contain arithmetic information about the representations of quadratic forms. It is n...
متن کاملThe Dialectic of Truth and Appearance in Lacan’s Reading of Gerhard Richter’s Overpainted-from-photographs
One of the most important contemporary theoretical approaches that can be used to analyze works of art is the theories of Jacques Lacan (1901-1980), a French post-structuralist psychoanalyst. By combining psychoanalysis, philosophy, linguistics, and anthropology, he analyzes the world of the human subject’s mind in a series of intertwined and extensive cultural and social relationships.This art...
متن کاملA Detailed Note on the Zeros of Eisenstein
The present paper is a detailed paper for the paper “On the zeros of Eisenstein series for Γ0(5) and Γ ∗ 0(7).” We locate almost all the zeros of the Eisenstein series associated with the Fricke groups Γ0(5) and Γ ∗ 0(7) in their fundamental domains by applying and expanding the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (“On the zeros of Eisenstein series”, 1970). We also use the a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008