On divisibility of the class number $h^+$ of the real cyclotomic fields of prime degree $l$

Author:
Stanislav Jakubec

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

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Abstract | References | Similar Articles | Additional Information

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

Article copyright:
© Copyright 1998
American Mathematical Society