On the spectral expansion of hyperbolic Eisenstein series

被引：10

作者：

Jorgenson, Jay ^{[2
]}

Kramer, Juerg ^{[1
]}

von Pippich, Anna-Maria ^{[1
]}

机构：

[1] Humboldt Univ, Inst Math, D-10099 Berlin, Germany

[2] CUNY City Coll, Dept Math, New York, NY 10031 USA

来源：

MATHEMATISCHE ANNALEN | 2010年 / 346卷 / 04期

基金：

美国国家科学基金会;

关键词：

Riemann Surface; Eisenstein Series; Fuchsian Group; Geodesic Path; Laurent Expansion;

D O I：

10.1007/s00208-009-0422-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we determine the spectral expansion, meromorphic continuation, and location of poles with identifiable singularities for the scalar-valued hyperbolic Eisenstein series. Similar to the form-valued hyperbolic Eisenstein series studied in Kudla and Millson (Invent Math 54:193-211, 1979), the scalar-valued hyperbolic Eisenstein series is defined for each primitive, hyperbolic conjugacy class within the uniformizing group associated to any finite volume hyperbolic Riemann surface. Going beyond the results in Kudla and Millson (Invent Math 54:193-211, 1979) and Risager (Int Math Res Not 41:2125-2146, 2004), we establish a precise spectral expansion for the hyperbolic Eisenstein series for any finite volume hyperbolic Riemann surface by first proving that the hyperbolic Eisenstein series is in L (2). Our other results, such as meromorphic continuation and determination of singularities, are derived from the spectral expansion.

引用

页码：931 / 947

页数：17

共 11 条

[1]

Chavel I., 1984, EIGENVALUES RIEMANNI

[2]

Falliero T, 2007, MATH ANN, V339, P341, DOI 10.1007/s00208-007-0116-0

[3]

Garbin D, 2008, COMMENT MATH HELV, V83, P701

[4]

Iwaniec H., 2002, Spectral Methods of Automorphic Forms, Vsecond