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arXiv · 1301.3051

Sur la théorie spectrale des métriques intégrables sur une surface de Riemann compacte

Mounir Hajli
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Abstract

We continue the study of the spectral theory associated to integrable metrics, started in our previous paper arXiv:1301.1793 [math.SP]. We introduce the notion of 1-integrable metric on line-bundles on a compact Riemann surface. We extend the spectral theory of generalized Laplacians to line-bundles equipped with 1-integrable metrics. As an application, we recover the following identity: [ζ'_{Δ_{\bar{\mathcal{O}(m)}_\infty}}(0)=T_g\bigl((\p^1,ω_\infty); \bar{\mathcal{O}(m)}_\infty \bigr),] obtained using direct computations in arXiv:1301.1792 [math.NT].

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Mounir Hajli. 2013-01-15. Sur la théorie spectrale des métriques intégrables sur une surface de Riemann compacte. https://arxiv.org/abs/1301.3051

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