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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Zeros of Dedekind zeta functions in the critical strip
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by Emmanuel Tollis PDF
Math. Comp. 66 (1997), 1295-1321 Request permission


In this paper, we describe a computation which established the GRH to height $92$ (resp. $40$) 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 $5$ and $6$, and statistics about the smallest zero of a number field.
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Additional Information
  • Emmanuel Tollis
  • Affiliation: 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
  • Email:
  • Received by editor(s): January 20, 1996
  • Received by editor(s) in revised form: March 10, 1996
  • © Copyright 1997 American Mathematical Society
  • Journal: Math. Comp. 66 (1997), 1295-1321
  • MSC (1991): Primary 11R42
  • DOI:
  • MathSciNet review: 1423079