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Selberg Zeta function and hyperbolic Eisenstein series.
- Source :
-
Communications in Contemporary Mathematics . Jun2024, Vol. 26 Issue 5, p1-73. 73p. - Publication Year :
- 2024
-
Abstract
- Let Γ be a Fuchsian group acting on the hyperbolic upper half-plane H , such that Γ \ H is a geometrically finite Riemann surface with respect to the natural hyperbolic metric induced from H. If γ is hyperbolic then following [J. Kudla and S. Millson, Harmonic differentials and closed geodesics on a Riemann surface, Invent. Math. 54 (1979) 193–211; J. D. Fay, Fourier coefficients of the resolvent for a Fuchsian group, J. Reine Angew. Math. 293 (1977) 143–203], there is a corresponding hyperbolic Eisenstein series. In this paper, we study the limiting behavior of hyperbolic Eisenstein series on a degenerating family of geometrically finite hyperbolic surfaces. In particular, we give a partial lightening to a question of Ji, concerning the approximation of Eisenstein series during degeneration (see Proposition 5.2 and Theorem 5.2). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02191997
- Volume :
- 26
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Communications in Contemporary Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 176558091
- Full Text :
- https://doi.org/10.1142/S0219199723500049