2000 年 23 巻 3 号 p. 345-357
We study the spectral zeta function ζM(s) associated with the spectrum of Laplacian acting on functions of a compact simply connected Riemannian symmetric space M of rank one and the spectral zeta function ζSnp, δ(s) associated with the spectrum of Laplacian acting on p-forms of the sphere Sn. We give the residues of ζM(s) and ζSnp(s) explicitly. For the odd dimensional sphere Sn, we show that ζSnp, δ(s) vanishes at negative integers.
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