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pro vyhledávání: '"Titus Hilberdink"'
Autor:
Titus Hilberdink
Publikováno v:
Journal of Number Theory. 236:261-279
In this paper we study how often the divisor function lies in a set 〈 P 〉 generated by a subset P of the primes by multiplication. We consider a variety of different sets P using results on the average behaviour of multiplicative functions by Wir
Autor:
Titus Hilberdink
Publikováno v:
Transactions of the American Mathematical Society. 374:7569-7588
Autor:
Titus Hilberdink, Ammar Ali Neamah
Publikováno v:
International Journal of Number Theory. 16:1005-1011
In this paper, we study the counting functions [Formula: see text], [Formula: see text] and [Formula: see text] of a generalized prime system [Formula: see text]. Here, [Formula: see text] is the partial sum of the Möbius function over [Formula: see
We study the Fredholm properties of Toeplitz operators acting on doubling Fock Hilbert spaces, and describe their essential spectra for bounded symbols of vanishing oscillation. We also compute the index of these Toeplitz operators in the special cas
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dad6c25d335dea99fc846c02eda22849
Autor:
Titus Hilberdink
In this paper, we study entire functions whose maximum on a disc of radius $r$ grows like $e^{h(\log r)}$ for some function $h(\cdot )$. We show that this is impossible if $h^{\prime \prime }(r)$ tends to a limit as $r\to \infty $, thereby solving a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d284675f05269e23333c08ecb7c6129b
https://centaur.reading.ac.uk/88558/1/entirefunctionpaper.pdf
https://centaur.reading.ac.uk/88558/1/entirefunctionpaper.pdf
Autor:
Titus Hilberdink
Publikováno v:
Linear Algebra and its Applications. 532:179-197
We study operators which have (infinite) matrix representation whose entries are multiplicative functions of two variables. We show that such operators are infinite tensor products over the primes. Applications to finding the eigenvalues explicitly o
Publikováno v:
International Journal of Number Theory
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c2d94b0423847fc326c9e8f23249422
https://hdl.handle.net/21.11116/0000-0005-E4CE-221.11116/0000-0005-E4D0-E21.11116/0000-0005-E4D1-D
https://hdl.handle.net/21.11116/0000-0005-E4CE-221.11116/0000-0005-E4D0-E21.11116/0000-0005-E4D1-D
Autor:
László Tóth, Titus Hilberdink
Publikováno v:
Journal of Number Theory. 169:327-341
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
Autor:
Titus Hilberdink
Publikováno v:
Linear and Multilinear Algebra. 65:813-829
We study the asymptotic behaviour of the singular values of matrices with entries $a_{ij}=f(i/j)$ if $j|i$ and zero otherwise,\ud with $f$ an arithmetical function. In particular, we study the case where $f$ is multiplicative and $F(x):=\sum_{n\leq x
Autor:
Titus Hilberdink
In this paper we study various "abscissae" which one can associate to a given function $f$, or rather to the power moments of $f$. These are motivated by long standing open problems in analytic number theory. We show how these abscissae connect to th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f635ea71c5999959fb8e9dfee8557cd5
https://centaur.reading.ac.uk/76912/1/powermoments.pdf
https://centaur.reading.ac.uk/76912/1/powermoments.pdf