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2001 On Artin L-Functions for Octic Quaternion Fields
Sami Omar
Experiment. Math. 10(2): 237-246 (2001).


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.


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Sami Omar. "On Artin L-Functions for Octic Quaternion Fields." Experiment. Math. 10 (2) 237 - 246, 2001.


Published: 2001
First available in Project Euclid: 30 August 2001

zbMATH: 1046.11083
MathSciNet: MR1837673

Primary: 11R42

Keywords: Artin L-functions , quaternion fields , Zeros

Rights: Copyright © 2001 A K Peters, Ltd.


Vol.10 • No. 2 • 2001
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