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On Zeros of the Derivative of the Selberg Zeta Function

Wenzhi Luo
American Journal of Mathematics
Vol. 127, No. 5 (Oct., 2005), pp. 1141-1151
Stable URL: http://www.jstor.org/stable/40068004
Page Count: 11
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On Zeros of the Derivative of the Selberg Zeta Function
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Abstract

In this work, we study the distribution of nontrivial zeros of the derivatives of Selberg zeta functions on cocompact hyperbolic surfaces, and obtain an asymptotic formula for the zero density with bounded height, which is an analogue of the Weyl law. We then relate the distribution of the zeros to the multiplicities of Laplacian eigenvalues.

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