MEROMORPHIC EXTENSIONS OF A CLASS OF ZETA FUNCTIONS FOR TWO-DIMENSIONAL BILLIARDS WITHOUT ECLIPSE

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Author(s)

    • MORITA TAKEHIKO
    • Department of Mathematics, Graduate School of Science, Hiroshima University

Abstract

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.

Journal

  • Tohoku Mathematical Journal, Second Series

    Tohoku Mathematical Journal, Second Series 59(2), 167-202, 2007

    Tohoku University

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