Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Hilberdink, Titus"'
Autor:
Hilberdink, Titus
In this paper we develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations. For example, $n+2\to 2n\to 2^n\to 2^{\cdot^
Externí odkaz:
http://arxiv.org/abs/2409.06661
Autor:
Broucke, Frederik, Hilberdink, Titus
In this paper we obtain a mean value theorem for a general Dirichlet series $f(s)= \sum_{j=1}^\infty a_j n_j^{-s}$ with positive coefficients for which the counting function $A(x) = \sum_{n_{j}\le x}a_{j}$ satisfies $A(x)=\rho x + O(x^\beta)$ for som
Externí odkaz:
http://arxiv.org/abs/2409.06301
We consider the family of arithmetical matrices given explicitly by $$E(\sigma,\tau)=\left\{\frac{n^\sigma m^\sigma}{[n,m]^\tau}\right\}_{n,m=1}^\infty,$$ where $[n,m]$ is the least common multiple of $n$ and $m$ and the real parameters $\sigma$ and
Externí odkaz:
http://arxiv.org/abs/2110.14323
Akademický článek
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Autor:
Neamah, Ammar Ali, Hilberdink, Titus W
Publikováno v:
International Journal of Number Theory, 2019
In this paper, we study the counting functions $\psi_\mathcal{P}(x)$, $N_\mathcal{P}(x)$ and $M_\mathcal{P}(x)$ of a generalized prime system $\mathcal{N}$. Here $M_\mathcal{P}(x)$ is the partial sum of the M\"{o}bius function over $\mathcal{N}$ not
Externí odkaz:
http://arxiv.org/abs/1901.06866
Publikováno v:
International Journal of Number Theory, Vol. 16, No. 1 (2020) 77-90
We use elementary arguments to prove results on the order of magnitude of certain sums concerning the gcd's and lcm's of $k$ positive integers, where $k\ge 2$ is fixed. We refine and generalize an asymptotic formula of Bordell\`{e}s (2007), and exten
Externí odkaz:
http://arxiv.org/abs/1805.10877
Autor:
Hilberdink, Titus, Tóth, László
Publikováno v:
Journal of Number Theory 169 (2016), 327-341
We deduce an asymptotic formula with error term for the sum $\sum_{n_1,\ldots,n_k \le x} f([n_1,\ldots, n_k])$, where $[n_1,\ldots, n_k]$ stands for the least common multiple of the positive integers $n_1,\ldots, n_k$ ($k\ge 2$) and $f$ belongs to a
Externí odkaz:
http://arxiv.org/abs/1604.04508
Autor:
Hilberdink, Titus W.1 (AUTHOR)
Publikováno v:
Journal of Number Theory. Apr2025, Vol. 269, p460-464. 5p.
Publikováno v:
J. Number Theory 166 (2016), 93-104
We prove that \[ \sum_{k,{\ell}=1}^N\frac{(n_k,n_{\ell})^{2\alpha}}{(n_k n_{\ell})^{\alpha}} \ll N^{2-2\alpha} (\log N)^{b(\alpha)} \] holds for arbitrary integers $1\le n_1<\cdots < n_N$ and $0<\alpha<1/2$ and show by an example that this bound is o
Externí odkaz:
http://arxiv.org/abs/1512.03758