Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation

There are two main interrelated goals of this paper. Firstly we investigate the sums

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Hlavní autoři: Beresnevich, Victor, Haynes, Alan, Velani, Sanju
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2020
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Continued fractions
Diophantine analysis
Diophantine approximation
metric theory of algorithms
Number theory
Probabilistic theory: distribution modulo
Ostrowski expansion
uniform distribution
Multiplicative Diophantine approximation
ISBN:9781470440954, 1470440954
ISSN:0065-9266, 1947-6221
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Abstract There are two main interrelated goals of this paper. Firstly we investigate the sums
AbstractList View the abstract.
There are two main interrelated goals of this paper. Firstly we investigate the sums
Author Velani, Sanju
Beresnevich, Victor
Haynes, Alan
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Keywords Ostrowski expansion
uniform distribution
Multiplicative Diophantine approximation
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Notes Includes bibliographical reference (p. 75-77)
January 2020, volume 263, number 1276 (sixth of 7 numbers)
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Snippet There are two main interrelated goals of this paper. Firstly we investigate the sums
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SubjectTerms Continued fractions
Diophantine analysis
Diophantine approximation
metric theory of algorithms
Number theory
Probabilistic theory: distribution modulo
TableOfContents Problems and main results -- Developing techniques and establishing the main results
Cover -- Title page -- Part 1 . Problems and main results -- Notation -- 1. Sums of reciprocals -- 2. Multiplicative Diophantine approximation -- Part 2 . Developing techniques and establishing the main results -- 3. Ostrowski expansion -- 4. Estimates for | - | -- 5. A gaps lemma and its consequences -- 6. Counting solutions to | - |&lt -- \ve -- 7. Establishing the homogeneous results on sums of reciprocals -- 8. Establishing the inhomogeneous results on sums of reciprocals -- 9. Proofs of Theorems 2.2, 2.3 and 2.4 -- 10. Proof of Theorem 2.1 -- Acknowledgments -- Bibliography -- Back Cover
Title Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation
URI https://www.ams.org/memo/1276/
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Volume 263
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