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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

Abstract:

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: jakubec@mau.savba.sk
  • 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: https://doi.org/10.1090/S0025-5718-98-00916-8
  • MathSciNet review: 1443121