Zeros of Dedekind zeta functions in the critical strip |
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Authors: | Emmanuel Tollis |
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Institution: | U.M.R. 9936 du C.N.R.S., U.F.R. de Mathématiques et Informatique, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France |
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Abstract: | In this paper, we describe a computation which established the GRH to height (resp. ) for cubic number fields (resp. quartic number fields) with small discriminant. We use a method due to E. Friedman for computing values of Dedekind zeta functions, we take care of accumulated roundoff error to obtain results which are mathematically rigorous, and we generalize Turing's criterion to prove that there is no zero off the critical line. We finally give results concerning the GRH for cubic and quartic fields, tables of low zeros for number fields of degree and , and statistics about the smallest zero of a number field. |
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Keywords: | Dedekind zeta function Generalized Riemann Hypothesis |
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