Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
MEROMORPHIC EXTENSIONS OF A CLASS OF ZETA FUNCTIONS FOR TWO-DIMENSIONAL BILLIARDS WITHOUT ECLIPSE
TAKEHIKO MORITA
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2007 年 59 巻 2 号 p. 167-202

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The main purpose of the present paper is to show that a class of dynamical zeta functions associated with the so-called two-dimensional open billiard without eclipse have meromorphic extensions to the half-plane consisting of all complex numbers whose real parts are greater than a certain negative number. As an application, we verify that the zeta function for the length spectrum of the corresponding billiard table has the same property.
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© 2007 by THE TOHOKU UNIVERSITY
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