Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation

Bibliographic Details
Call Number:Libro Electrónico
Main Author: Beresnevich, Victor
Other Authors: Haynes, Alan, Velani, Sanju
Format: Electronic eBook
Language:Inglés
Published: Providence : American Mathematical Society, 1920.
Series:Memoirs of the American Mathematical Society Ser.
Subjects:
Continued fractions.
Diophantine analysis.
Number theory.
Fractions continues.
Analyse diophantienne.
Théorie des nombres.
Continued fractions
Diophantine analysis
Number theory
Number theory > Probabilistic theory: distribution modulo $1$; metric theory of algorithms > Diophantine approximation [See also 11Jxx].
Number theory > Probabilistic theory: distribution modulo $1$; metric theory of algorithms > General theory of distribution modulo $1$ [See also 11J71].
Number theory > Probabilistic theory: distribution modulo $1$; metric theory of algorithms > Irregularities of distribution, discrepancy [See also 11Nxx].
Number theory > Probabilistic theory: distribution modulo $1$; metric theory of algorithms > Metric theory of continued fractions [See also 11A55, 11J70].
Number theory > Elementary number theory {For analogues in number fields, see 11R04} > Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15].
Number theory > Diophantine approximation, transcendental number theory [See also 11K60] > Small fractional parts of polynomials and generalizations.
Number theory > Diophantine approximation, transcendental number theory [See also 11K60] > Continued fractions and generalizations [See also 11A55, 11K50].
Number theory > Diophantine approximation, transcendental number theory [See also 11K60] > Distribution modulo one [See also 11K06].
Number theory > Diophantine approximation, transcendental number theory [See also 11K60] > Inhomogeneous linear forms.
Number theory > Diophantine approximation, transcendental number theory [See also 11K60] > Metric theory.
Online Access:Texto completo
Table of Contents:
  • 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 |
  • |<\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

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