Hausdorff dimension of sets arising in number theory.

*(English)*Zbl 0575.28004Number theory, Semin. New York 1983-84, Lect. Notes Math. 1135, 1-8 (1985).

[For the entire collection see Zbl 0553.00003.]

Expository paper, explaining the method used by the author [J. Reine Angew. Math. 331, 192-206 (1982; Zbl 0468.10032)], in particular, for his estimate on the Hausdorff dimension of the set of real numbers with partial quotients 1 or 2, and the relation of this method to the work of other authors. He expresses his hope that the scope of this method of ”spectral analysis” will reach beyond the usual number-theoretical applications.

Reviewer: B.Volkmann

##### MSC:

28A12 | Contents, measures, outer measures, capacities |

11J70 | Continued fractions and generalizations |

28A75 | Length, area, volume, other geometric measure theory |

11K16 | Normal numbers, etc. |

11K55 | Metric theory of other number-theoretic algorithms and expansions |