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Localization of the first zero of the Dedekind zeta function


Author: Sami Omar
Journal: Math. Comp. 70 (2001), 1607-1616
MSC (2000): Primary 11R42
DOI: https://doi.org/10.1090/S0025-5718-01-01305-9
Published electronically: March 7, 2001
MathSciNet review: 1836922
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Abstract:

Using Weil's explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totally complex fields of degree less than or equal to 30 having the smallest known discriminant.


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Additional Information

Sami Omar
Affiliation: Laboratoire d’Algorithmique Arithmétique, Université Bordeaux I, 351 cours de la Libération, F-33405 Talence Cedex France
Email: omar@math.u-bordeaux.fr

DOI: https://doi.org/10.1090/S0025-5718-01-01305-9
Keywords: Dedekind zeta function, zeros, discriminants
Received by editor(s): June 4, 1999
Received by editor(s) in revised form: February 1, 2000
Published electronically: March 7, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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