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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A formula for the discriminant of number fields


Authors: Pei-Chu Hu and Zhuan Ye
Journal: Proc. Amer. Math. Soc. 139 (2011), 2007-2008
MSC (2010): Primary 11R42
Published electronically: November 2, 2010
MathSciNet review: 2775377
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Abstract: We obtain a formula for the discriminant $ D_{\kappa/\mathbb{Q}}$ of an algebraic number field $ \kappa$ in terms of a ratio of the first two coefficients of the Taylor series of $ \zeta_\kappa$ at $ 1/2$.


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Additional Information

Pei-Chu Hu
Affiliation: Department of Mathematics, Shandong University, Jinan 250100, Shandong, People’s Republic of China
Email: pchu@sdu.edu.cn

Zhuan Ye
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: ye@math.niu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10546-4
PII: S 0002-9939(2010)10546-4
Keywords: Number field, Dedekind $\zeta$-function, discriminant, generalized Riemann hypothesis
Received by editor(s): January 4, 2010
Received by editor(s) in revised form: June 9, 2010
Published electronically: November 2, 2010
Additional Notes: The first author was partially supported by the Natural Science Foundation of China
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.