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arXiv · 1301.1792

Sur la fonction Zêta associée au Laplacien singulier $Δ_{{\mathcal{O}(m)}_\infty}$

Mounir Hajli
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Abstract

In a previous paper, we computed the spectrum of the singular Laplacian attached to canonical metrics on $\mathbb{P}^1$. In this article, we study $ζ_\infty$, the Zeta function associated to this spectrum. We prove that it admits a meromorphic continuation to $\mathbb{C}$. Moreover, this continuation is holomorphic at zero. We compute $ζ_\infty(0)$ and $ζ'_\infty(0)$.

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BibTeXRIS

Mounir Hajli. 2013-01-16. Sur la fonction Zêta associée au Laplacien singulier $Δ_{{\mathcal{O}(m)}_\infty}$. https://doi.org/10.1016/j.jnt.2013.06.007

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