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

Jakubec, Stanislav

doi:10.1090/S0025-5718-98-00916-8

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