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Eisenstein Cohomology and the Construction of p-Adic Analytic L-Functions

Published online by Cambridge University Press:  04 December 2007

Joachim Mahnkopf
Affiliation:
Max-Planck-Institut für Mathematik, P.O. Box 7280, 53072 Bonn, Germany. E-mail: [email protected]
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Abstract

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Let π be a cuspidal automorphic representation of GL3($\Bbb A$$\Bbb Q$), unramified at p and of cohomological type at infinity. We construct p-adic L-functions, which interpolate the critical values of L(π,s) and which satisfy a logarithmic growth condition. We obtain these functions as p-adic Mellin transforms of certain distributions μπ on $\Bbb Z$p* having values in some fixed number field and which are of moderate growth. In the p-ordinary case we obtain the bound |μπ(U)|p[les ]|μHaar(U)|p for open subsets U[les ] $\Bbb Z$p*, where μHaar denotes the invariant distribution on $\Bbb Z$p*.

Type
Research Article
Copyright
© 2000 Kluwer Academic Publishers