Ankeny-Artin-Chowla conjecture and continued fraction expansion

Authors
Hashimoto, R
Citation
R. Hashimoto, Ankeny-Artin-Chowla conjecture and continued fraction expansion, J NUMBER TH, 90(1), 2001, pp. 143-153
Citations number
8
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF NUMBER THEORY
ISSN journal
0022314X → ACNP
Volume
90
Issue
1
Year of publication
2001
Pages
143 - 153
Database
ISI
SICI code
0022-314X(200109)90:1<143:ACACFE>2.0.ZU;2-#
Abstract
For any prime p congruent to I modulo 4, let (t + u rootp)/2 be the fundame ntal unit of Q(rootp). Then Ankeny, Artin, and Chowla conjectured that it i s not divisible by p. In this paper, we investigate a certain relation betw een the conjecture and the continued fraction expansion of (1 + rootp)/2, C onsequently, we prove that the conjecture is true if p is not "small" in so me sense. (C) 2001 Academic Press.