Mathematical Research Letters

Volume 21 (2014)

Number 2

The p-adic Shintani cocycle

Pages: 403 – 422

DOI: http://dx.doi.org/10.4310/MRL.2014.v21.n2.a14

Author

G. Ander Steele (Department of Mathematics, University of Calgary, Alberta, Canada)

Abstract

The Shintani cocycle on $\mathrm{GL}_n(\mathbb{Q})$, 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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