Rational approximations to linear forms of exponentials and binomials
Gregory V. Chudnovsky · Proceedings of the National Academy of Sciences · 1983
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.