Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation

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

Saved in:
Bibliographic Details
Main Authors Beresnevich, Victor, Haynes, Alan, Velani, Sanju
Format eBook Book
LanguageEnglish
Published Providence, Rhode Island American Mathematical Society 2020
Edition1
SeriesMemoirs of the American Mathematical Society
Subjects
Continued fractions
Diophantine analysis
Diophantine approximation
metric theory of algorithms
Number theory
Probabilistic theory: distribution modulo
Ostrowski expansion
uniform distribution
Multiplicative Diophantine approximation
Online AccessGet full text
ISBN9781470440954
1470440954
ISSN0065-9266
1947-6221
DOI10.1090/memo/1276

Cover

Table of Contents:
  • 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