p-adic measures attached to automorphic representations of GL(3)
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.
symmetric squares of \(\ell \)-adic representations
scientific article; zbMATH DE number 4071010
scientific article