Affordable Access

Numbers with good factorization properties

Authors
Publication Date
Disciplines
  • Law
  • Mathematics

Abstract

Numbers with good factorization properties Séminaire Delange-Pisot-Poitou. Théorie des nombres WLADYSLAWNARKIEWICZ Numbers with good factorization properties Séminaire Delange-Pisot-Poitou. Théorie des nombres, tome 13, no 2 (1971-1972), exp. no 13, p. 1-3. <http://www.numdam.org/item?id=SDPP_1971-1972__13_2_A1_0> © Séminaire Delange-Pisot-Poitou. Théorie des nombres (Secrétariat mathématique, Paris), 1971-1972, tous droits réservés. L’accès aux archives de la collection « Séminaire Delange-Pisot-Poitou. Théorie des nombres » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 13-01 NUMBERS WITH GOOD FACTORIZATION PROPERTIES by Wladyslaw HARKIEWICZ Séminaire DELANGE-PISOT-POITOU (Theorie des nombres) 1 3e année, 1971/72, n° 13, 3 p. 7 février 1972 1. - ( 1~ ~.3; [2]) shown that ~-~~,,~- 5 ~ the simplest quadratic field with non-trivial class-group, almost no algebraic integer has unique factori- zation, that is to say, if F(x) denotes the number of non-associated integers 0’ with x , which have unique factorization, to.en F(x)/x tends to zero. He proved also, that the same holds for the number H(x) of natural numbers n ~ x with unique factorization in 9,(,~-~ 5~ . In fact, analogous results are true for all fields with non-trivial class-groups, as shown in [4], 16 1. For F(x) , one gets evaluations of the form whereas similar evaluations for H(x) are obtained only for nornal. So we get the first question, , QUESTION I. - Is the evaluation H~x~ x~lo~‘.~ x ~a ~ > 0), true for all fields K with non-trivial class-group ? 2. - In 1960, L. observed, that in an algebraic number field IL with the class-number h(K) ~

There are no comments yet on this publication. Be the first to share your thoughts.