Displaying similar documents to “Sums involving Farey fractions”

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.

The distribution of the sum-of-digits function

Michael Drmota, Johannes Gajdosik (1998)

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.