The absolute continuity of a limit law for Sylvester series

Janos Galambos

Displaying similar documents to “The absolute continuity of a limit law for Sylvester series”

A simple proof of the mean fourth power estimate for $ζ (\frac{1}{2} + i t)$ and $L (\frac{1}{2} + i t, χ)$

K. Ramachandra (1974)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Dirichlet series of $ζ (s) ζ^{α} (s + 1) f (s + 1)$ : On an error term associated with its coefficients

U. Balakrishnan, Y.-F. S. Pétermann (1996)

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The distribution of values of the Euler function

Paul Bateman (1972)

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On an estimate of Walfisz and Saltykov for an error term related to the Euler function

Y.-F. S. Pétermann (1998)

Journal de théorie des nombres de Bordeaux

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The technique developed by A. Walfisz in order to prove (in 1962) the estimate $H (x) ≪ {(log x)}^{2 / 3} {(log log x)}^{4 / 3}$ for the error term $H (x) = \sum_{n \leq x} \frac{φ (n)}{n} - \frac{6}{π^{2}} x$ related to the Euler function is extended. Moreover, the argument is simplified by exploiting works of A.I. Saltykov and of A.A. Karatsuba. It is noted in passing that the proof proposed by Saltykov in 1960 of $H (x) ≪ {(log x)}^{2 / 3} {(log log x)}^{1 + ϵ}$ is erroneous and once corrected “only” yields Walfisz’ result. The generalizations obtained can be applied to error terms related to various classical - and less classical -...

On sums of sequences of integers, I

A. Balog, András Sárközy (1984)

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Uniform distribution mod 1 (II)

H Kesten (1962)

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On the metric theory of continued fractions

I. Aliev, S. Kanemitsu, A. Schinzel (1998)

Colloquium Mathematicae

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On the speed of convergence of the Oppenheim series

J. Galambos (1971)

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The Zeckendorf expansion of polynomial sequences

Michael Drmota, Wolfgang Steiner (2002)

Journal de théorie des nombres de Bordeaux

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In the first part of the paper we prove that the Zeckendorf sum-of-digits function $s_{z} (n)$ and similarly defined functions evaluated on polynomial sequences of positive integers or primes satisfy a central limit theorem. We also prove that the Zeckendorf expansion and the $q$ -ary expansions of integers are asymptotically independent.