## 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