Abstract
We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums), and in the global case (for instance, Dirichlet L-functions, involving in particular the study of inverse Mellin transforms); we also give a number of little-known but very useful numerical methods, usually but not always related to the computation of L-functions.
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Notes
- 1.
The definition of J given below is a sum over all \(x\in {\mathbb F}_q\), so that \(J(\varepsilon ,\varepsilon )=q^2\) and not \((q-2)^2\).
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Cohen, H. (2019). Computational Number Theory in Relation with L-Functions. In: Inam, I., Büyükaşık, E. (eds) Notes from the International Autumn School on Computational Number Theory. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-12558-5_3
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DOI: https://doi.org/10.1007/978-3-030-12558-5_3
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