Abstract
Using Weil explicit Formulas, we show how to compute the multiplicity n χ of a zero at the point \(\frac{1}{2}\) of the Artin L-functions associated to a character χ of Degree 2 in quaternion fields of degree 8. We prove in several examples that n χ = 0 when W(χ) and n χ = 1 when W(χ) = −1.
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© 2000 Springer-Verlag Berlin Heidelberg
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Omar, S. (2000). Central Values of Artin L-Functions for Quaternion Fields. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_29
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DOI: https://doi.org/10.1007/10722028_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67695-9
Online ISBN: 978-3-540-44994-2
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