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.
"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