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arXiv · 1209.5018

The $p$-adic Shintani cocycle

G. Ander Steele
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Abstract

The Shintani cocycle on $\GL_n(\Q)$, as constructed by Hill, gives a cohomological interpretation of special values of zeta functions for totally real fields of degree $n$. We give an explicit criterion for a specialization of the Shintani cocycle to be $p$-adically interpolable. As a corollary, we recover the results of Deligne-Ribet, Cassou Noguès and Barsky on the construction of $p$-adic $L$-functions attached to totally real fields.

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G. Ander Steele. 2012-09-26. The $p$-adic Shintani cocycle. https://arxiv.org/abs/1209.5018

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