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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Dyadic methods in the measure theory of numbers
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by R. C. Baker PDF
Trans. Amer. Math. Soc. 221 (1976), 419-432 Request permission

Abstract:

Some new theorems in metric diophantine approximation are obtained by dyadic methods. We show for example that if ${m_1},{m_2}, \ldots$, are distinct integers with ${m_n} = O({n^p})$ then ${\Sigma _{n \leqslant N}}e({m_n}x) = O({N^{1 - q}})$ except for a set of x of Hausdorff dimension at most $(p + 4q - 1)/(p + 2q)$; and that for any sequence of intervals ${I_1},{I_2}, \ldots$ in [0, 1) the number of solutions of $\{ {x^n}\} \in {I_n}\;(n \leqslant N)$ is a.e. asymptotic to ${\Sigma _{n \leqslant N}}|{I_n}|(x > 1)$.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 221 (1976), 419-432
  • MSC: Primary 10K15; Secondary 10K05
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0417097-6
  • MathSciNet review: 0417097