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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 | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

  • 1. Pei-Chu Hu and Chung-Chun Yang, Value distribution theory related to number theory, Birkhäuser Verlag, Basel, 2006. MR 2245631
  • 2. A. M. Odlyzko, Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results, Sém. Théor. Nombres Bordeaux (2) 2 (1990), no. 1, 119–141 (English, with French summary). MR 1061762

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Additional Information

Pei-Chu Hu
Affiliation: Department of Mathematics, Shandong University, Jinan 250100, Shandong, People’s Republic of China

Zhuan Ye
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115

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.