Title: Chapter I Diophantine Approximations to Real Numbers
Abstract: Publisher SummaryThis chapter discusses Diophantine approximations to real numbers. A great number of problems in the theory of Diophantine approximations can be set in the following form. Let λ1…., λn be n real numbers and ɛ a positive real number. For fixed λ1…., λn, the dependence on ɛ of the function T has a deep connection with the badly approximable real numbers. The chapter presents a study of harmonious sets and their uses in harmonic analysis. It also presents some simple and powerful techniques that will be very useful in the study of badly approximable real numbers and discusses Minkowski's theorem that provides the solution of homogeneous linear Diophantine problems.
Publication Year: 1972
Publication Date: 1972-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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