zbMATH — the first resource for mathematics

On the error-sum function of Lüroth series. (English) Zbl 1154.11331
Summary: We introduce the error-sum function of Lüroth series. Some elementary properties of this function are studied. We also determine the Hausdorff dimension of the graph of this function.

11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
11J83 Metric theory
Full Text: DOI
[1] Barrionuevo, J.; Burton, R.M.; Dajani, K.; Kraaikamp, C., Ergodic properties of generalized Lüroth series, Acta arith., 74, 311-327, (1996) · Zbl 0848.11039
[2] Dajani, K.; Kraaikamp, C., On approximation by Lüroth series, J. théor. nombres Bordeaux, 8, 331-346, (1996) · Zbl 0870.11039
[3] Dajani, K.; Kraaikamp, C., Ergodic theory of numbers, Carus mathematical monographs, vol. 29, (2002), Math. Assoc. Amer. Washington, DC · Zbl 1033.11040
[4] Falconer, K.J., Fractal geometry, mathematical foundations and application, (1990), Wiley, Ltd. Chichester
[5] Falconer, K.J., Techniques in fractal geometry, (1997), Wiley, Ltd. Chichester · Zbl 0869.28003
[6] Galambos, J., Representations of real numbers by infinite series, Lecture notes in math., vol. 502, (1976), Springer Berlin/New York · Zbl 0322.10002
[7] Jager, H.; De Vroedt, C., Lüroth series and their ergodic properties, Proc. K. nederl. akad. wet. A, 72, 31-42, (1969) · Zbl 0167.32201
[8] Ridley, J.N.; Petruska, G., The error-sum function of continued fraction, Indag. math. (N.S.), 11, 273-282, (2000) · Zbl 0989.11006
[9] Schweiger, F., Ergodic theory of fibred systems and metric number theory, (1995), Clarendon Press Oxford · Zbl 0819.11027
[10] Vervaat, W., Success epochs in Bernoulli trials, Mathematical center tracts, vol. 42, (1972), Mathematisch Centrum Amsterdam · Zbl 0267.60003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.