On Artin L-Functions for Octic Quaternion Fields
Omar, Sami
Experiment. Math., Tome 10 (2001) no. 3, p. 237-246 / Harvested from Project Euclid
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We study the Artin L-function L(s, χ) associated to the unique character χ of degree 2 in quaternion fields of degree 8. We first explain how to find examples of quaternion octic fields with not too large a discriminant. We then develop a method using a quick compuation of the order n*#967; of the zero of L(s, χ) at the point s = 1/2. In all our calculations, we find that nχ only depends on the sign of the root number W(χ); indeed nχ = 0 when W (χ) = -1. Finally we give some estimates on nχ and low zeros of L(s, χ) on the critical line in terms fo the Artin conductor *#402;χ of the character χ.
Publié le : 2001-05-14
Classification:  Artin L-functions,  zeros,  quaternion fields,  11R42 
@article{999188634,
     author = {Omar, Sami},
     title = {On Artin L-Functions for Octic Quaternion Fields},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 237-246},
     language = {en},
     url = {http://dml.mathdoc.fr/item/999188634}
}

Omar, Sami. On Artin L-Functions for Octic Quaternion Fields. Experiment. Math., Tome 10 (2001) no. 3, pp.  237-246. http://gdmltest.u-ga.fr/item/999188634/