Sums of reciprocals of fractional parts and multiplicative diophantine approximation

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Title:

Sums of reciprocals of fractional parts and multiplicative diophantine approximation

Author:

Beresnevich, Victor, 1971- author.

ISBN:

9781470456603

Personal Author:

Beresnevich, Victor, 1971- author.

Physical Description:

1 online resource (92 pages).

Series:

Memoirs of the American Mathematical Society ; volume 263, number 1276

Memoirs of the American Mathematical Society ; volume 263, number 1276.

General Note:

"January 2020, volume 263, number 1276 (sixth of 7 numbers)."

Contents:

Sums of reciprocals -- Multiplicative Diophantine approximation -- Ostrowski expansion -- Estimates for n[alpha] - [gamma] -- A gaps lemma and its consequences -- Counting solutions to n[alpha] - [gamma] < [epsilon] -- Establishing the homogeneous results on sums of reciprocals -- Establishing the inhomogeneous results on sums of reciprocals -- Proofs of theorems 2.2, 2.3 and 2.4 -- Proof of theorem 2.1.

Local Note:

Electronic reproduction. Ann Arbor, MI : ProQuest, 2018. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.

Subject Term:

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.

Continued fractions.

Diophantine analysis.

Number theory -- Diophantine approximation, transcendental number theory [See also 11K60] -- Continued fractions and generalizations [See also 11A55, 11K50].