p-adic measures attached to automorphic representations of GL(3). (English) Zbl 0656.10023

The object of this paper is the L-function that is defined by the symmetric squares of \(\ell\)-adic representations (these form a compatible system of 3-dimensional \(\ell\)-adic representations for the Galois group of \({\bar {\mathbb{Q}}}\) over \({\mathbb{Q}})\). This L-function is interpreted as the twisted L-function of a certain automorphic representation of GL(3).
For an “ordinary” prime p (i.e. the p-th Fourier coefficient of the corresponding primitive cusp form of weight \(\geq 2\) for the congruence subgroup \(\Gamma_ 0(N)\) is a p-adic unit and p does not divide N) the author constructs a p-adic analogue of this twisted L-function and proves its p-adic holomorphy and functional equation.
The essential part of the paper is the p-adic interpolation of all critical values.
Reviewer: N.V.Kuznetsov


11F33 Congruences for modular and \(p\)-adic modular forms
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F80 Galois representations
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