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Vidéo Année : 2017

A. von Pippich - An analytic class number type formula for PSL2(Z)

Afficher 

Jérémy Magnien
  • Fonction : Réalisateur
  • PersonId : 966327

Résumé

For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H instead of prime numbers. In this talk, we report on a formula that determines the special value at s=1 of the derivative of the Selberg zeta function for Γ=PSL2(Z). This formula is obtained as an application of a generalized Riemann-Roch isometry for the trivial sheaf on ¯¯¯¯¯¯¯¯¯¯¯Γ∖H, equipped with the Poincaré metric. This is joint work with Gerard Freixas.

Dates et versions

medihal-01721477 , version 1 (02-03-2018)

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  • HAL Id : medihal-01721477 , version 1

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Anna von Pippich, Jérémy Magnien. A. von Pippich - An analytic class number type formula for PSL2(Z): Summer School 2017 - Arakelov Geometry and diophantine applications. 2017. ⟨medihal-01721477⟩
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