Orbits of algebraic numbers with low heights

Author:
Gregory P. Dresden

Journal:
Math. Comp. **67** (1998), 815-820

MSC (1991):
Primary 11R04, 11R06; Secondary 12D10

DOI:
https://doi.org/10.1090/S0025-5718-98-00963-6

MathSciNet review:
1468942

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the two smallest values of are and , for 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 of the American Mathematical Society*
with MSC (1991):
11R04,
11R06,
12D10

Retrieve articles in all journals with MSC (1991): 11R04, 11R06, 12D10

Additional Information

**Gregory P. Dresden**

Affiliation:
Department of Mathematics, Washington & Lee University, Lexington, Virginia 24450

Email:
dresdeng@wlu.edu

DOI:
https://doi.org/10.1090/S0025-5718-98-00963-6

Received by editor(s):
September 30, 1996

Additional Notes:
I am very grateful for the assistance and guidance of my advisor, Dr. Vaaler.

Article copyright:
© Copyright 1998
American Mathematical Society