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Probabilistic diophantine approximation: randomness in lattice point counting

This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of i...

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Detalles Bibliográficos
Autor principal: Beck, József
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-10741-7
http://cds.cern.ch/record/1968848
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author Beck, József
author_facet Beck, József
author_sort Beck, József
collection CERN
description This book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques. Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.
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spelling cern-19688482021-04-21T20:49:36Zdoi:10.1007/978-3-319-10741-7http://cds.cern.ch/record/1968848engBeck, JózsefProbabilistic diophantine approximation: randomness in lattice point countingMathematical Physics and MathematicsThis book gives a comprehensive treatment of random phenomena and distribution results in diophantine approximation, with a particular emphasis on quadratic irrationals. It covers classical material on the subject as well as many new results developed by the author over the past decade. A range of ideas from other areas of mathematics are brought to bear with surprising connections to topics such as formulae for class numbers, special values of L-functions, and Dedekind sums. Care is taken to elaborate difficult proofs by motivating major steps and accompanying them with background explanations, enabling the reader to learn the theory and relevant techniques. Written by one of the acknowledged experts in the field, Probabilistic Diophantine Approximation is presented in a clear and informal style with sufficient detail to appeal to both advanced students and researchers in number theory.Springeroai:cds.cern.ch:19688482014
spellingShingle Mathematical Physics and Mathematics
Beck, József
Probabilistic diophantine approximation: randomness in lattice point counting
title Probabilistic diophantine approximation: randomness in lattice point counting
title_full Probabilistic diophantine approximation: randomness in lattice point counting
title_fullStr Probabilistic diophantine approximation: randomness in lattice point counting
title_full_unstemmed Probabilistic diophantine approximation: randomness in lattice point counting
title_short Probabilistic diophantine approximation: randomness in lattice point counting
title_sort probabilistic diophantine approximation: randomness in lattice point counting
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-10741-7
http://cds.cern.ch/record/1968848
work_keys_str_mv AT beckjozsef probabilisticdiophantineapproximationrandomnessinlatticepointcounting