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Computational aspects of Artin \(L\)-functions. (English) Zbl 1337.11030

Campillo, Antonio (ed.) et al., Zeta functions in algebra and geometry. Second international workshop, Universitat de les Illes Balears, Palma de Mallorca, Spain, May 3–7, 2010. Proceedings. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (ISBN 978-0-8218-6900-0/pbk). Contemporary Mathematics 566, 3-20 (2012).
Summary: Galois representations are a special type of algebraic arithmetical objects to which one can associate \(L\)-functions. The aim of this paper is the description of a procedure to calculate as many coefficients as needed of exotic Artin \(L\)-functions from the explicit resolution of some Galois embedding problems.
Contents: Introduction. 1. Modular forms and Maass forms. 2. Weight one holomorphic modular forms. 3. Some character tables. 4. Artin \(L\)-functions. 5. Modular forms of weight one and Artin \(L\)-functions. 6. Linear and projective Galois representations. 7. Computation of Artin L-functions. References.
For the entire collection see [Zbl 1242.11004].

MSC:

11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F11 Holomorphic modular forms of integral weight
11F32 Modular correspondences, etc.
12F12 Inverse Galois theory
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