A function related to the central limit theorem

Paul Bracken

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On the rearranged block-orthonormal systems.

Nadibaidze, G. (2000)

Georgian Mathematical Journal

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On a Relation Between Sums of Arithmetical Functions and Dirichlet Series

Hideaki Ishikawa, Yuichi Kamiya (2012)

Publications de l'Institut Mathématique

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On convergence subsystems of orthonormal systems.

Bareladze, G. (1994)

Georgian Mathematical Journal

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Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values

Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2009)

Journal de Théorie des Nombres de Bordeaux

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We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.

Discrepancy estimates for a class of normal numbers

Yoshinobu Nakai, Iekata Shiokawa (1992)

Acta Arithmetica

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Counterexamples on non- $α$ -normal functions with good integrability.

Aulaskari, Rauno, Makhmutov, Shamil, Rättyä, Jouni (2011)

The New York Journal of Mathematics [electronic only]

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Sign changes of error terms related to arithmetical functions

Paulo J. Almeida (2007)

Journal de Théorie des Nombres de Bordeaux

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Let $H (x) = \sum_{n \leq x} \frac{φ (n)}{n} - \frac{6}{π^{2}} x$ . Motivated by a conjecture of Erdös, Lau developed a new method and proved that $# {n \leq T : H (n) H (n + 1) < 0} ≫ T .$ We consider arithmetical functions $f (n) = \sum_{d ∣ n} \frac{b_{d}}{d}$ whose summation can be expressed as $\sum_{n \leq x} f (n) = α x + P (log (x)) + E (x)$ , where $P (x)$ is a polynomial, $E (x) = - \sum_{n \leq y (x)} \frac{b_{n}}{n} ψ (\frac{x}{n}) + o (1)$ and $ψ (x) = x - ⌊ x ⌋ - 1 / 2$ . We generalize Lau’s method and prove results about the number of sign changes for these error terms.

Displaying similar documents to “A function related to the central limit theorem”

On the rearranged block-orthonormal systems.

On a Relation Between Sums of Arithmetical Functions and Dirichlet Series

On convergence subsystems of orthonormal systems.

Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values

Discrepancy estimates for a class of normal numbers

Counterexamples on non- α -normal functions with good integrability.

Sign changes of error terms related to arithmetical functions

Counterexamples on non- $α$ -normal functions with good integrability.