Heights of algebraic numbers and Szegő's theorem

Author:
Wayne Lawton

Journal:
Proc. Amer. Math. Soc. **49** (1975), 47-50

MSC:
Primary 12D10; Secondary 10F30

MathSciNet review:
0376628

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the present paper we derive an algorithm which yields approximations to the height of an algebraic number. The techniques are analytical and are motivated by prediction theoretic concepts.

**[1]**P. E. Blanksby and H. L. Montgomery,*Algebraic integers near the unit circle*, Acta Arith.**18**(1971), 355–369. MR**0296021****[2]**Rufus Bowen,*Entropy for group endomorphisms and homogeneous spaces*, Trans. Amer. Math. Soc.**153**(1971), 401–414. MR**0274707**, 10.1090/S0002-9947-1971-0274707-X**[3]**J. W. S. Cassels,*An introduction to Diophantine approximation*, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR**0087708****[4]**Philip J. Davis,*Interpolation and approximation*, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR**0157156****[5]**H. Dym and H. P. McKean,*Fourier series and integrals*, Academic Press, New York-London, 1972. Probability and Mathematical Statistics, No. 14. MR**0442564****[6]**Einar Hille,*Analytic function theory. Vol. 1*, Introduction to Higher Mathematics, Ginn and Company, Boston, 1959. MR**0107692****[7]**Serge Lang,*Diophantine geometry*, Interscience Tracts in Pure and Applied Mathematics, No. 11, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR**0142550****[8]**Wayne Lawton,*The structure of compact connected groups which admit an expansive automorphism*, Recent advances in topological dynamics (Proc. Conf., Yale Univ., New Haven, Conn., 1972; in honor of Gustav Arnold Hedlund), Springer, Berlin, 1973, pp. 182–196. Lecture Notes in Math., Vol. 318. MR**0391051****[9]**D. H. Lehmer,*Factorization of certain cyclotomic functions*, Ann. of Math. (2)**34**(1933), no. 3, 461–479. MR**1503118**, 10.2307/1968172

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
12D10,
10F30

Retrieve articles in all journals with MSC: 12D10, 10F30

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0376628-X

Keywords:
Height of algebraic number,
Hilbert space,
Gram determinant,
Jensen's theorem,
Szegö's theorem

Article copyright:
© Copyright 1975
American Mathematical Society