Results 41 to 50 of about 56 (55)

Using a parity-sensitive sieve to count prime values of a polynomial. [PDF]

Proc Natl Acad Sci U S A, 1997
Friedlander J, Iwaniec H.
europepmc   +1 more source

Tissue engineering of cultured skin substitutes. [PDF]

J Cell Mol Med, 2005
Horch RE, Kopp J, Kneser U, Beier J, Bach AD.   +4 more
europepmc   +1 more source

CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES

CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES
In this paper, we first give a brief survey on the theory of meromorphic continuation and natural boundaries of multiple Dirichlet series. Then we consider the double Dirichlet series Φ2(s) defined by the convolution of logarithmic derivatives of the Riemann zeta-function.
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Diced Costal Cartilage for Augmentation Rhinoplasty.

Chin Med J (Engl), 2015
Ma JG, Wang KM, Zhao XH, Cai L, Li X.
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On certain sums involving von Mangoldt's function in short intervals

, 1980
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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 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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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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