通过退化的Loxodromic eisenstein系列

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2019-01-01 DOI:10.2206/kyushujm.73.357

Y. Irie

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引用次数: 0

摘要

对于有限Kleinian群的loxodrom元，定义了loxodrom Eisenstein级数。它类似于与尖端相关的普通爱森斯坦级数。研究了有限体积三维双曲流形退化序列的渐近性。特别地，我们证明了如果直线元对应于退化的测地线，那么相应的直线爱森斯坦级数收敛于极限流形上新发展的顶点对应的普通爱森斯坦级数。

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LOXODROMIC EISENSTEIN SERIES THROUGH DEGENERATION

The loxodromic Eisenstein series is defined for a loxodromic element of cofinite Kleinian groups. It is the analogue of the ordinary Eisenstein series associated to cusps. We study the asymptotic behavior of the loxodromic Eisenstein series for degenerating sequences of three-dimensional hyperbolic manifolds of finite volume. In particular, we prove that if the loxodromic element corresponds to the degenerating geodesic, then the associated loxodromic Eisenstein series converges to the ordinary Eisenstein series associated to the newly developing cusp on the limit manifold.

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.