General Formalism

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter I in Introduction to Diophantine Approximations, 1995, pp 1-19 from Springer

Abstract: Abstract We are interested in the following problem. Given an irrational number α, determine all solutions of the inequality with integers q, p, or more generally, of an inequality where Ψ is some positive decreasing function of a real variable. If ξ is a real number, we may write ∥ξ∥ for the distance between ξ and the nearest integer. Then |qα — p| = ∥qα∥ whenever it is sufficiently small, and we may rewrite the fundamental inequality (1) in the form ∥qα∥

Date: 1995
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DOI: 10.1007/978-1-4612-4220-8_1

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