Shintani cocyles and vanishing order of $p$-adic Hecke $L$-series at $s=0$

Details Shintani cocyles and vanishing order of $p$-adic Hecke $L$-series at $s=0$ Shintani cocyles and vanishing order of $p$-adic Hecke $L$-series at $s=0$

2012-03-30

arxiv.org/abs/1203.6689v2

Mathematics

Number Theory

Scientific paper

Let $\chi$ be a Hecke character of finite order of a totally real number field $F$. By using Hill's Shintani cocyle we provide a cohomological construction of the $p$-adic $L$-series $L_p(\chi, s)$ associated to $\chi$. This is used to show that $L_p(\chi, s)$ has a trivial zero at $s=0$ of order at least equal to the number of places of $F$ above $p$ where the local component of $\chi$ is trivial.

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