Representations of real numbers by infinite series
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Publication:1223332
DOI10.1007/BFb0081642zbMath0322.10002MaRDI QIDQ1223332
Publication date: 1976
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Other number representations (11A67) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11Kxx)
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The Hausdorff dimension of sets of numbers defined by their \(Q\)-Cantor series expansions ⋮ On the exceptional sets in Erdös–Rényi limit theorem of β-expansion ⋮ The growth speed for the product of consecutive digits in Lüroth expansions ⋮ Chaotic sets and Hausdorff dimension for Lüroth expansions ⋮ Unnamed Item ⋮ Khintchine's constant for Lüroth representation ⋮ Uniform distribution of sequences connected with arithmetical functions ⋮ Hausdorff dimension of certain sets arising in Engel continued fractions ⋮ Unnamed Item ⋮ Dimension of level sets in GCF expansion with parameters ⋮ Hausdorff dimension of certain sets arising in Engel expansions ⋮ Law of large numbers and the central limit theorem for sequences of coefficients of rotational expansions ⋮ Singularity and absolute continuity of measures associated with the rotation of a circle ⋮ Exceptional sets related to the largest digits in Lüroth expansions ⋮ Hausdorff dimensions of certain sets in terms of the Sylvester series ⋮ ON SOME EXCEPTIONAL SETS IN ENGEL EXPANSIONS AND HAUSDORFF DIMENSIONS ⋮ On the longest block in Lüroth expansion ⋮ On the Lebesgue measure of sum-level sets for Lüroth expansion ⋮ Convergence results for Oppenheim expansions. II ⋮ Some distribution results of the Oppenheim continued fractions ⋮ Unnamed Item ⋮ Normality of different orders for Cantor series expansions ⋮ DESCRIPTIVE COMPLEXITY IN CANTOR SERIES ⋮ Hausdorff dimensions of some exceptional sets in Engel expansions ⋮ On singularity of distribution of random variables with independent symbols of Oppenheim expansions ⋮ Localized growth speed of the digits in Engel expansions ⋮ On the $G$-isomorphism of probability and dimensional theories of representations of real numbers and fractal faithfulness of systems of coverings ⋮ On the error-sum function of pierce expansions ⋮ New asymptotic results for generalized Oppenheim expansions ⋮ Level sets of partial maximal digits for Lüroth expansion ⋮ Dimension theory of Lüroth digits ⋮ Extrema of Luroth Digits and a zeta function limit relation ⋮ Alternate Base Numeration Systems ⋮ The generalized shifts and rational numbers ⋮ \(G\)-representation of real numbers and some of its applications ⋮ The convergence exponent and the well approximated sets for Lüroth expansion ⋮ HAUSDORFF DIMENSIONS OF SOME EXCEPTIONAL SETS IN THE FIRST OSTROGRADSKY SERIES ⋮ SLOW GROWTH RATE OF THE DIGITS IN ENGEL EXPANSIONS ⋮ FINITE PATTERN PROBLEMS RELATED TO LÜROTH EXPANSION ⋮ ON LÜROTH EXPANSIONS IN WHICH THE LARGEST DIGIT GROWS WITH SLOWLY INCREASING SPEED ⋮ A Salem generalised function ⋮ Some types of numeral systems and their modeling ⋮ A class of Cantor sets associated with the regular continued fractions ⋮ How many points have the same Engel and Sylvester expansions? ⋮ THE GROWTH RATE OF THE DIGITS IN THE LÜROTH EXPANSIONS ⋮ The relative growth rate for the digits in Lüroth expansions ⋮ On the growth speed of digits in Engel expansions ⋮ A NOTE ON THE RELATIVE GROWTH RATE OF THE MAXIMAL DIGITS IN LÜROTH EXPANSIONS ⋮ Unnamed Item ⋮ Metrical properties for a class of continued fractions with increasing digits ⋮ Positive additive functions with respect to interval filling sequences, and some sequences of integers with gap conditions ⋮ Some remarks on the generalized St. Petersburg games and formal Laurent series expansions ⋮ Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C 2 - Transformations ⋮ Number theoretic applications of a class of Cantor series fractal functions. 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