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On the standard L-functions of central-simple algebras

✍ Scribed by Kâzım Ilhan Ikeda

Publisher
Elsevier Science
Year
2000
Tongue
French
Weight
95 KB
Volume
124
Category
Article
ISSN
0007-4497

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✦ Synopsis

In this article, we investigate (up to Q) the values of the standard Lfunction L M m (K) (s, Ψ ) of the algebra M m (K) over a CM-field K attached to a certain Hecke character of K (defined through a Hecke character ψ of the maximal totally real subfield F of K) at s = (k + 2n)/η(k); where m k ∈ Z is fixed and depends on the character ψ, ∀n ∈ Z + .

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A splitting field of a central simple algebra is said to be absolute Galois if it is Galois over some fixed subfield of the centre of the algebra. The paper proves an existence theorem for such fields over global fields with enough roots of unity. As an application, all twisted function fields and a