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arXiv · 2407.01269

La m\'ethode de Shintani et ses variantes

Pierre Colmez
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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. 2024-07-01. La m\'ethode de Shintani et ses variantes. https://arxiv.org/abs/2407.01269

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