Proceedings of the Japan Academy, Series A, Mathematical Sciences

The first eigenvalue problem and tensor products of zeta functions

Shin-ya Koyama

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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.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 5 (2004), 35-39.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116442239

Digital Object Identifier
doi:10.3792/pjaa.80.35

Mathematical Reviews number (MathSciNet)
MR2062796

Zentralblatt MATH identifier
1065.11035

Subjects
Primary: 11F72: Spectral theory; Selberg trace formula
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Keywords
Selberg Conjecture zeta functions automorphic $L$-functions multiple zeta functions tensor products the first eigenvalue

Citation

Koyama, Shin-ya. The first eigenvalue problem and tensor products of zeta functions. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 5, 35--39. doi:10.3792/pjaa.80.35. https://projecteuclid.org/euclid.pja/1116442239


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