## Displaying similar documents to “On the asymmetric divisor problem with congruence conditions”

### Sign changes of error terms related to arithmetical functions

Journal de Théorie des Nombres de Bordeaux

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Let $H\left(x\right)={\sum }_{n\le x}\frac{\phi \left(n\right)}{n}-\frac{6}{{\pi }^{2}}x$. Motivated by a conjecture of Erdös, Lau developed a new method and proved that $#\left\{n\le T:H\left(n\right)H\left(n+1\right)<0\right\}\gg T.$ We consider arithmetical functions $f\left(n\right)={\sum }_{d\mid n}\frac{{b}_{d}}{d}$ whose summation can be expressed as ${\sum }_{n\le x}f\left(n\right)=\alpha x+P\left(log\left(x\right)\right)+E\left(x\right)$, where $P\left(x\right)$ is a polynomial, $E\left(x\right)=-{\sum }_{n\le y\left(x\right)}\frac{{b}_{n}}{n}\psi \left(\frac{x}{n}\right)+o\left(1\right)$ and $\psi \left(x\right)=x-⌊x⌋-1/2$. We generalize Lau’s method and prove results about the number of sign changes for these error terms.

### On the counting function for the generalized Niven numbers

Journal de Théorie des Nombres de Bordeaux

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Given an integer base $q\ge 2$ and a completely $q$-additive arithmetic function $f$ taking integer values, we deduce an asymptotic expression for the counting function ${N}_{f}\left(x\right)=#\left\{0\le n<x\phantom{\rule{0.166667em}{0ex}}|\phantom{\rule{0.166667em}{0ex}}f\left(n\right)\mid n\right\}$ under a mild restriction on the values of $f$. When $f={s}_{q}$, the base $q$ sum of digits function, the integers counted by ${N}_{f}$ are the so-called base $q$ Niven numbers, and our result provides a generalization of the asymptotic known in that case.

### Extremal problems in the class of delta-subharmonic functions of finite order in a half-plane.

Sibirskij Matematicheskij Zhurnal

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### Unsteady flow of a dusty fluid through an inclined open rectangular channel.

Acta Universitatis Apulensis. Mathematics - Informatics

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### The generalized Morawetz problem for Lavrent'ev-Bitsadze equation with spectral parameter.

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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### Stability problems for linear differential and difference systems

Archivum Mathematicum

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In this paper, there are derived sufficient conditions for exponential and asymptotic stability of differential and difference systems.