Zeros of Dedekind zeta functions in the critical strip-Reference-Cited by-同舟云学术

Zeros of Dedekind zeta functions in the critical strip

Published:1997 Issue:219 Volume:66 Page:1295-1321
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Tollis Emmanuel

Abstract

In this paper, we describe a computation which established the GRH to height 92 92 (resp. 40 40 ) 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 5 5 and 6 6 , and statistics about the smallest zero of a number field.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1997-66-219/S0025-5718-97-00871-5/S0025-5718-97-00871-5.pdf

Reference21 articles.

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