Multidimensional Continued Fractions
Multidimensional Continued Fractions

Author: Fritz Schweiger

Publisher: Oxford University Press, USA

Published: 2000

Total Pages: 250

ISBN-13: 9780198506867

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Mathematician Fritz Schweiger, whose academic affiliation is not provided, provides an introduction to a field of research that has seen remarkable progress in recent decades, concentrating on multidimensional continued fractions which can be described by fractional linear maps or equivalently by a set of (n + 1) x (n + 1) matrices. Addressing the question of periodicity, he refines the problem of convergence to the question of whether these algorithms give "good" simultaneous Diophantine approximations. He notes that these algorithms are not likely to provide such "good" approximations which satisfy the n-dimensional Dirichlet property. Also studied are the ergodic properties of these maps. Annotation copyrighted by Book News Inc., Portland, OR

The Story of Algebraic Numbers in the First Half of the 20th Century
The Story of Algebraic Numbers in the First Half of the 20th Century

Author: Władysław Narkiewicz

Publisher: Springer

Published: 2019-01-18

Total Pages: 448

ISBN-13: 3030037541

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The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.