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Hausdorff dimension of sets arising in number theory. (English) Zbl 0575.28004
Number 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
28A12Contents, measures, outer measures, capacities
11J70Continued fractions and generalizations
28A75Length, area, volume, other geometric measure theory
11K16Normal numbers, etc.
11K55Metric theory of other number-theoretic algorithms and expansions