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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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Real cyclotomic fields of prime conductor and their class numbers
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by John C. Miller PDF
Math. Comp. 84 (2015), 2459-2469 Request permission


Surprisingly, the class numbers of cyclotomic fields have only been determined for fields of small conductor, e.g., for prime conductors up to 67, due to the problem of finding the “plus part,” i.e., the class number of the maximal real subfield. Our results have improved the situation. We prove that the plus part of the class number is 1 for prime conductors between 71 and 151. Also, under the assumption of the generalized Riemann hypothesis, we determine the class number for prime conductors between 167 and 241. This technique generalizes to any totally real field of moderately large discriminant, allowing us to confront a large class of number fields not previously treatable.
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Additional Information
  • John C. Miller
  • Affiliation: Department of Mathematics, Rutgers University, Hill Center for the Mathematical Sciences, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
  • MR Author ID: 1074298
  • Email:
  • Received by editor(s): October 28, 2013
  • Received by editor(s) in revised form: December 13, 2013
  • Published electronically: February 5, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2459-2469
  • MSC (2010): Primary 11R29, 11R18; Secondary 11R80, 11Y40
  • DOI:
  • MathSciNet review: 3356035