Metrical problems concerning continued fractions

C. de Vroedt

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Linear independence of continued fractions

Jaroslav Hančl (2002)

Journal de théorie des nombres de Bordeaux

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The main result of this paper is a criterion for linear independence of continued fractions over the rational numbers. The proof is based on their special properties.

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H. Kesten (1964)

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The distribution of the sum-of-digits function

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Journal de théorie des nombres de Bordeaux

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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.

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Normalizing constants for a statistic based on logarithms of disjoint m-spacings

Franciszek Czekała (1996)

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J. Mikusiński (1953)

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C. Hooley (1963)

Acta Arithmetica

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A variant of Selberg's asymptotic formula.

Catalina Calderón García, María José Zárate Azcuna (1990)

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On partitions without small parts

J.-L. Nicolas, A. Sárközy (2000)

Journal de théorie des nombres de Bordeaux

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Let $r (n, m)$ denote the number of partitions of $n$ into parts, each of which is at least $m$ . By applying the saddle point method to the generating series, an asymptotic estimate is given for $r (n, m)$ , which holds for $n \to \infty$ , and $1 \leq m \leq c_{1} \frac{n}{{(log n)}^{c_{2}}}$ .