La méthode de Shintani et ses variantes

Published 1 Jul 2024 in math.NT | (2407.01269v1)

Abstract: We give several versions of Shintani's method for the decomposition into simplicial cones of the fundamental domain of a torus modulo a lattice, and we investigate some applications to the study of Hecke $L$-functions at integer points. In particular, we prove the analytic class number formula for a totally real field, directly at $s=0$.

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Pierre Colmez

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