Bohr sets and multiplicative Diophantine approximation

Preprint, Other literature type English OPEN
Chow, Sam;
  • Publisher: Duke University Press
  • Journal: issn: 0012-7094
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1215/00127094-2018-0001
  • Subject: Mathematics - Combinatorics | 11J20 | 11H06 | metric Diophantine approximation | geometry of numbers | 52C05 | 11J83, 11J20, 11H06, 52C05 | additive combinatorics | Mathematics - Number Theory | 11J83
    arxiv: Mathematics::Number Theory

In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem, sharpening and making unconditional a result recently obtained conditi... View more
  • References (19)
    19 references, page 1 of 2

    [1] C. Aistleitner, A note on the Duffin-Schaeffer conjecture with slow divergence, Bull. Lond. Math. Soc. 46 (2014), 64-168.

    [2] V. Beresnevich, G. Harman, A. Haynes and S. Velani, The Duffin-Schaeffer conjecture with extra divergence II, Math. Z. 275 (2013), 127-133.

    [3] V. Beresnevich, A. Haynes and S. Velani, Sums of reciprocals of fractional parts and multiplicative Diophantine approximation, arXiv:1511.06862.

    [4] V. Beresnevich, F. Ram´ırez and S. Velani, Metric Diophantine Approximation: some aspects of recent work, Dynamics and Analytic Number Theory, London Math. Soc. Lecture Note Ser. (N.S.) 437, Cambridge University Press, 2016, pp. 1-95.

    [5] V. Beresnevich and S. Velani, A note on three problems in metric Diophantine approximation, Recent Trends in Ergodic Theory and Dynamical Systems, Contemp. Math. 631 (2015), 211-229.

    [6] R. J. Duffin and A. C. Schaeffer, Khintchine's problem in metric Diophantine approximation, Duke Math. J. 8 (1941), 243-255.

    [7] P. X. Gallagher, Approximation by reduced fractions, J. Math. Soc. Japan 13 (1961), 342-345.

    [8] P. X. Gallagher, Metric simultaneous diophantine approximation, J. Lond. Math. Soc. 37 (1962), 387-390.

    [9] G. Harman, Metric number theory, London Math. Soc. Lecture Note Ser. (N.S.) 18, Clarendon Press, Oxford 1998.

    [10] A. Haynes, A. Pollington and S. Velani, The Duffin-Schaeffer Conjecture with extra divergence, Math. Ann. 353 (2012), 259-273.

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