Proceedings of the American Mathematical Society

Author(s): Jun Wu
Journal: Proc. Amer. Math. Soc. 134 (2006), 1631-1634.
MSC (2000): Primary 11K50, 11J70
Posted: December 15, 2005
Retrieve article in: PDF

Abstract: We prove that the set of Lévy constants for quadratic irrationals is dense in $[\log \frac{\sqrt{5}+1}{2}, \infty)$ .

1.: C. Baxa, Extremal values of continuants and transcendence of certain continued fractions, Adv. in Appl. Math., 32 (2004), no. 4, 754-790. MR 2053844 (2005f:11141)
2.: C. Faivre, Distribution of Lévy constants for quadratic numbers, Acta Arith., 61 (1992), no. 1, 13-34. MR 1153919 (93c:11057)
3.: E. P. Golubeva, The spectrum of Lévy constants for quadratic irrationalities, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 263 (2000), Anal. Teor. Chisel i Teor. Funkts. 16, 20-33, 237, translation in J. Math. Sci. (New York) 110 (2002), no. 6, 3040-3047. MR 1756334 (2001b:11065)
4.: H. Jager and P. Liardet, Distributions arithmétiques des dénominateurs des convergents de fraction continues, Indag. Math., 50 (1988), 181-197. MR 0952514 (89i:11085)
5.: A. Ya. Khintchine, Continued Fractions, P. Noordhoff, Groningen, The Netherlands, 1963. MR 0161834 (28:5038)
6.: P. Lévy, Sur les lois de probabilité dont dépendent les quotients complets et incomplets d'une fraction continue, Bull. Soc. Math., 57 (1929), 178-194.
7.: J. Wu, A remark on the growth of the denominators of convergents, preprint.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11K50, 11J70

Jun Wu
Affiliation: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, People's Republic of China
Email: wujunyu@public.wh.hb.cn

DOI: 10.1090/S0002-9939-05-08283-3
PII: S 0002-9939(05)08283-3
Keywords: L\'evy constant, quadratic irrational
Received by editor(s): January 28, 2005
Posted: December 15, 2005
Additional Notes: The author was supported in part by the Kua-Shi-Ji Foundation of Educational Committee and NSFC (10571138). This work was done during the author's visit to the LAMFA, CNRS UMR 6140, Amiens; he would like to thank the institution for their warm hospitality.
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS