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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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On divisibility of the class number $h^+$ of the real cyclotomic fields of prime degree $l$
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by Stanislav Jakubec PDF
Math. Comp. 67 (1998), 369-398 Request permission


In this paper, criteria of divisibility of the class number $h^+$ of the real cyclotomic field $\mathbf {Q}(\zeta _p+\zeta _p^{-1})$ of a prime conductor $p$ and of a prime degree $l$ by primes $q$ the order modulo $l$ of which is $\frac {l-1}{2}$, are given. A corollary of these criteria is the possibility to make a computational proof that a given $q$ does not divide $h^+$ for any $p$ (conductor) such that both $\frac {p-1}{2},\frac {p-3}{4}$ are primes. Note that on the basis of Schinzel’s hypothesis there are infinitely many such primes $p$.
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Additional Information
  • Stanislav Jakubec
  • Affiliation: Mathematical Institute of the Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
  • Email:
  • Received by editor(s): March 16, 1995
  • Received by editor(s) in revised form: April 12, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 369-398
  • MSC (1991): Primary 11R29
  • DOI:
  • MathSciNet review: 1443121