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On certain sums involving von Mangoldt's function in short intervals

, 1980
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On Sums of Sums Involving the Von Mangoldt Function

Results in Mathematics
In the paper under review, the authors estimate the following sum over the von Mangoldt function, for the values \(k=1,2\) and large real numbers \(x\) and \(y\), \[ S_{k}(x,y):=\sum _{n\le y}\left( \sum _{q\le x}\sum _{d|\gcd(n,q)}d\Lambda \left( \frac{q}{d}\right) \right) ^{k}.
Isao Kiuchi, Wataru Takeda
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Exponential sums formed with the von Mangoldt function and Fourier coefficients of $${ GL}(m)$$ G L ( m ) automorphic forms

Monatshefte für Mathematik, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yujiao Jiang, Guangshi Lü
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On fractional sum of the von Mangoldt function

Colloquium Mathematicum
The paper under review belongs to a long line of articles dealing with sums of the shape \[ S_f (x) := \sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right), \] where \(\lfloor t \rfloor\) is the integer part of \(t\) and \(f\) is any usual arithmetic function.
Lü, Xiaodong, Xu, Xinyue
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CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES

Number Theory, 2007
SHIGEKI EGAMI, KOHJI MATSUMOTO
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On the von Mangoldt-type function of the Fibonacci zeta function

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Gaspar Mora, Luis M. Navas, Juan L. Varona   +2 more
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UNEXPECTED AVERAGE VALUES OF GENERALIZED VON MANGOLDT FUNCTIONS IN RESIDUE CLASSES

Journal of the Australian Mathematical Society, 2020
AbstractIn order to study integers with few prime factors, the average of $\unicode[STIX]{x1D6EC}_{k}=\unicode[STIX]{x1D707}\ast \log ^{k}$ has been a central object of research. One of the more important cases, $k=2$, was considered by Selberg [‘An elementary proof of the prime-number theorem’, Ann. of Math. (2)50 (1949), 305–313].
NICOLAS ROBLES, ARINDAM ROY
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Asymptotic behaviors of some arithmetic function associated with the von Mangoldt function

Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2023
Some function associated with the von Mangoldt function is investigated. It is related to the logarithm of the Riemann zeta function. By means of probability theory, we show that this function is bounded above and below by a certain function. It is possible that the result extends to Dirichlet series.
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On a sum involving the Mangoldt function

Periodica Mathematica Hungarica, 2020
Jie Wu
exaly