Title Sums of Reciprocals of Fractional Parts and Multiplicative Diophantine Approximation

Published Providence : American Mathematical Society, 1920

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Description 1 online resource (92 p.) Series Memoirs of the American Mathematical Society Ser. ; v.263 Memoirs of the American Mathematical Society Ser 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 Notes Description based upon print version of record Back Cover View the abstract Subject Continued fractions. Diophantine analysis. Number theory. 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. Form Electronic book Author Haynes, Alan Velani, Sanju ISBN 9781470456603 1470456605

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