2 research outputs found
On the appearance of Eisenstein series through degeneration
Let be a Fuchsian group of the first kind acting on the hyperbolic
upper half plane , and let be the
associated finite volume hyperbolic Riemann surface. If is parabolic,
there is an associated (parabolic) Eisenstein series, which, by now, is a
classical part of mathematical literature. If 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
corresponds to a degenerating hyperbolic element, then a
multiple of the associated hyperbolic Eisenstein series converges to parabolic
Eisenstein series on the limit surface.Comment: 15 pages, 2 figures. This paper has been accepted for publication in
Commentarii Mathematici Helvetic
Authenticity in college English textbooks - An intercultural perspective
10.1177/003368820203300203RELC Journal33258-8