ON DIVISIBILITY OF THE CLASS NUMBER h + OF THE REAL CYCLOTOMIC FIELDS OF PRIME DEGREE l

Abstract. In this paper, criteria of divisibility of the class number h + of the real cyclotomic field Q(ζp + ζ−1 p) of a prime conductor p and of a prime degree l by primes q the order modulo l of which is l−1, are given. A corollary of 2 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 p−1 p−3, are primes. 2 4 Note that on the basis of Schinzel’s hypothesis there are infinitely many such primes p