A Polya Operator for Automorphic L-functions
نویسنده
چکیده
Let k be a number field and letM be a simple k-algebra with center k of rank n, i.e. dimk(M) = n 2. Fix a k-involution x 7→ xτ on M , i.e. (xy)τ = yτxτ as well as (xτ )τ = x and xτ = x when x ∈ k. We will assume that M and τ are defined over the ring of integers O of k. The standard example will be the algebra of n× n matrices Matn(k) and x τ = xt the transposed matrix. For any ringR over k letM(R) = M⊗kR and letG be the k-groupscheme of invertible elements, i.e. G(R) = M(R)×. For almost all places v of k we have M(kv) ∼= Matn(kv). In this case we say that M splits at v. At any splitting place v we assume a Ov-isomorphism M(kv) → Matn(kv) fixed, wher Ov is the local ring of integers. Let A = Af × A∞ be the ring of adeles of k where Af is the finite and A∞ the infinite adeles. Let dx denote the additive Haar-measure on A given
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تاریخ انتشار 1999