Mathematics of Computation

Author(s): Gregory P. Dresden.
Journal: Math. Comp. 67 (1998), 815-820.
MSC (1991): Primary 11R04, 11R06; Secondary 12D10
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract: We prove that the two smallest values of $h(\alpha ) + h(\frac{1}{1-\alpha }) + h(1 - \frac{1}{\alpha })$ are $0$

and $0.4218\dots$ , for $\alpha$ any algebraic integer.

1.: E. Bombieri, A van der Poorten, and J. Vaaler, Effective measures of irrationality for cubic extensions of number fields, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 23 (1996), 211-248. CMP 97:08
2.: D. Boyd, Speculations concerning the range of Mahler's Measure, Canad. Math. Bull. 24 (4) (1981), 453-469. MR 83h:12002
3.: E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arithmetica 34 (1979), 391-401. MR 80i:10040
4.: D. H. Lehmer, Factorization of certain cyclotomic funcions, Ann. of Math. 34 (1933), 461-479.
5.: C. Pinner and J. Vaaler, The number of irreducible factors of a polynomial, I, Trans. Amer. Math. Soc. 339 (1993), 809-834. MR 93m:11108
6.: U. Rausch, On a theorem of Dobrowolski about the product of conjugate numbers, Colloquium Mathematicum 50 (1985), 137-142. MR 87i:11144
7.: D. Zagier, Algebraic numbers close to both 0 and 1, Mathematics of Computation 61 (203) (1993), 485-491. MR 94c:11104
8.: S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. (2) 136 (3) (1992), 569-587. MR 93j:14024

Retrieve articles in Mathematics of Computation with MSC (1991): 11R04, 11R06, 12D10

Gregory P. Dresden
Affiliation: Department of Mathematics, Washington & Lee University, Lexington, Virginia 24450
Email: dresdeng@wlu.edu

DOI: 10.1090/S0025-5718-98-00963-6
PII: S 0025-5718(98)00963-6
Received by editor(s): September 30, 1996
Additional Notes: I am very grateful for the assistance and guidance of my advisor, Dr. Vaaler.
Copyright of article: Copyright 1998, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6842(e) ISSN 0025-5718(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 2008, American Mathematical Society Privacy Statement		Search the AMS