Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Andreas Weingartner"'
Autor:
Andreas Weingartner
Publikováno v:
Proceedings of the American Mathematical Society. 149:4699-4708
We extend the Siegel-Walfisz theorem to a family of integer sequences that are characterized by constraints on the size of the prime factors. Besides prime powers, this family includes smooth numbers, almost primes and practical numbers.
11 page
11 page
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85f7629f1138f40742b371c7933ed20d
https://doi.org/10.1090/proc/15607
https://doi.org/10.1090/proc/15607
Autor:
Montserrat BATLLE RIBAS, Thomas BERNARD, Eyal BRILL, Maria Rosario COELHO, Maria Fátima COIMBRA, Jochen DEUERLEIN, Peter GATTINESI, Philipp HOHENBLUM, Pierre PIERONNE, Jordi RAICH, Luís SIMAS, Rui TEIXEIRA, Rita UGARELLI, Andreas WEINGARTNER, Monica CARDARILLI, Georgios GIANNOPOULOS
Publikováno v:
Techniques d'analyse.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::efeda123cce12aef1338c6602b1ecbdf
https://doi.org/10.51257/a-v1-p4244
https://doi.org/10.51257/a-v1-p4244
Autor:
Andreas Weingartner
Publikováno v:
International Journal of Number Theory. 16:629-638
An integer $n\ge 1$ is said to be practical if every natural number $ m \le n$ can be expressed as a sum of distinct positive divisors of $n$. The number of practical numbers up to $x$ is asymptotic to $c x/\log x$, where $c$ is a constant. In this n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30012429491cfc973c7f8ba91c1bdd2d
https://doi.org/10.1142/s1793042120500311
https://doi.org/10.1142/s1793042120500311
Autor:
Andreas Weingartner
We show that for integers $n$, whose ratios of consecutive divisors are bounded above by an arbitrary constant, the normal order of the number of prime factors is $C \log \log n$, where $C=(1-e^{-\gamma})^{-1} = 2.280...$ and $\gamma$ is Euler's cons
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a0124ac4625542d3e6d1f64f310a664d
http://arxiv.org/abs/2101.11585
http://arxiv.org/abs/2101.11585
Publikováno v:
Finite Fields and Their Applications. 44:22-33
Given a polynomial g of positive degree over a finite field, we show that the proportion of polynomials of degree n, which can be written as h + g k , where h is an irreducible polynomial of degree n and k is a nonnegative integer, has order of magni
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c7d51025bf29e9c8da09a617d856269b
https://doi.org/10.1016/j.ffa.2016.11.002
https://doi.org/10.1016/j.ffa.2016.11.002
Autor:
Andreas Weingartner, Carl Pomerance
A number $n$ is practical if every integer in $[1,n]$ can be expressed as a subset sum of the positive divisors of $n$. We consider the distribution of practical numbers that are also shifted primes, improving a theorem of Guo and Weingartner. In add
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a1bf2e3ce20516f3eef77c8d76923c6d
Autor:
Andreas Weingartner
Publikováno v:
Mathematika. 63:213-229
Let $\theta$ be an arithmetic function and let $\mathcal{B}$ be the set of positive integers $n=p_1^{\alpha_1} \cdots p_k^{\alpha_k}$, which satisfy $p_{j+1} \le \theta ( p_1^{\alpha_1}\cdots p_{j}^{\alpha_{j}})$ for $0\le j < k$. We show that $\math
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d86b46bb9935203b879d14aead4f46af
https://doi.org/10.1112/s002557931600022x
https://doi.org/10.1112/s002557931600022x
Autor:
Joshua Culver, Andreas Weingartner
We give an asymptotic estimate for the number of partitions of a set of $n$ elements, whose block sizes avoid a given set $\mathcal{S}$ of natural numbers. As an application, we derive an estimate for the number of partitions of a set with $n$ elemen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::96e50bd4420a4ce8a9419b9ce18d6157
http://arxiv.org/abs/1806.02316
http://arxiv.org/abs/1806.02316
Autor:
Andreas Weingartner
We establish formulas for the constant factor in several asymptotic estimates related to the distribution of integer and polynomial divisors. The formulas are then used to approximate these factors numerically.
22 pages, 5 tables
22 pages, 5 tables
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c3025ab928a76a4ab17206af4b87d41c
http://arxiv.org/abs/1705.06349
http://arxiv.org/abs/1705.06349
Autor:
Andreas Weingartner
Publikováno v:
Journal of Number Theory. 142:211-222
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9fc3d04a569825ea7e015d9bf64071c9
https://doi.org/10.1016/j.jnt.2014.02.021
https://doi.org/10.1016/j.jnt.2014.02.021