Rational approximations to linear forms of exponentials and binomials.

Abstract:

:Mahler proved the following quantitative result supplementing the Lindemann-Weierstrass theorem: Sigma(i=0) (n)C(i)e(ri) > H(-n-epsilon) for any distinct rational numbers r(0),r(1),..., r(n) and rational integers C(0),C(1),...,C(n) with H = max(0 1 - epsilon. The simplest examples of new numbers with the irrationality exponent "2 + epsilon" are sinh 1 or sin 1.

authors

Chudnovsky GV

doi

10.1073/pnas.80.10.3138

subject

Has Abstract

pub_date

1983-05-01 00:00:00

pages

3138-41

issue

10

eissn

0027-8424

issn

1091-6490

journal_volume

80

pub_type

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