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May 2004 The first eigenvalue problem and tensor products of zeta functions
Shin-ya Koyama
Proc. Japan Acad. Ser. A Math. Sci. 80(5): 35-39 (May 2004). DOI: 10.3792/pjaa.80.35

Abstract

We obtain a new bound for the first eigenvalue of the Laplacian for Bianchi manifolds by the method of Luo, Rudnick and Sarnak. We use a recent result of Kim on symmetric power $L$-functions. The key idea is to take tensor products of zeta functions, and we report on our recent developments on Kurokawa's multiple zeta functions.

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Shin-ya Koyama. "The first eigenvalue problem and tensor products of zeta functions." Proc. Japan Acad. Ser. A Math. Sci. 80 (5) 35 - 39, May 2004. https://doi.org/10.3792/pjaa.80.35

Information

Published: May 2004
First available in Project Euclid: 18 May 2005

zbMATH: 1065.11035
MathSciNet: MR2062796
Digital Object Identifier: 10.3792/pjaa.80.35

Subjects:
Primary: 11F72
Secondary: 11M06

Keywords: automorphic $L$-functions , multiple zeta functions , Selberg Conjecture , Tensor products , the first eigenvalue , zeta functions

Rights: Copyright © 2004 The Japan Academy

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Vol.80 • No. 5 • May 2004
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