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pro vyhledávání: '"Bordell��s, Olivier"'
Autor:
Bordell��s, Olivier, T��th, L��szl��
We obtain asymptotic formulas for the sums $\sum_{n_1,\ldots,n_k\le x} f((n_1,\ldots,n_k))$ and $ \sum_{n_1,\ldots,n_k\le x} f([n_1,\ldots,n_k])$ involving the gcd and lcm of the integers $n_1,\ldots,n_k$, where $f$ belongs to certain classes of addi
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https://explore.openaire.eu/search/publication?articleId=doi_________::775e1b961665b0ddac8e3fd9720151d1
Autor:
Bordell��s, Olivier, T��th, L��szl��
We unify in a large class of additive functions the results obtained in the first part of this work. The proof rests on series involving the Riemann zeta function and certain sums of primes which may have their own interest.
19 pages; comments a
19 pages; comments a
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https://explore.openaire.eu/search/publication?articleId=doi_________::709224d8cfda02cd977b2a8bc9c9fb63
Autor:
Bordell��s, Olivier
We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when $f = \Lambda$ and $f = \tau$, and provid
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70ec9f73f633da72698e6076e08c5294
http://arxiv.org/abs/2009.05751
http://arxiv.org/abs/2009.05751
Autor:
Bordell��s, Olivier
We first study the mean value of certain restricted divisor sums involving the Chowla-Walum sums, improving in particular a recent estimate given by Iannucci. The aim of the second part of this work is the generalization of the previous study, by res
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ecdd8ee5f885418ae92235b64a8a16ba
http://arxiv.org/abs/1910.14633
http://arxiv.org/abs/1910.14633
Autor:
Bordell��s, Olivier
We study a unitary analog to Redheffer's matrix. It is first proved that the determinant of this matrix is the unitary analogue to that of Redheffer's matrix. We also show that the coefficients of the characteristic polynomial may be expressed as sum
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dc41e4fbd6c0577fcfa7eb9233df5e77
http://arxiv.org/abs/1905.11183
http://arxiv.org/abs/1905.11183
Autor:
Bordell��s, Olivier, Cloitre, Benoit
Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
Comment: 10 pages
Comment: 10 pages
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::18318688f49d3e0d4b25cc3734bcc6ab
http://arxiv.org/abs/1804.05332
http://arxiv.org/abs/1804.05332
Autor:
Bordell��s, Olivier
Using estimates on Hooley's $\Delta$-function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic functions over short segments. Numerous examples are also given.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5042dab0d591f89b41a197f741e725e9
http://arxiv.org/abs/1605.00072
http://arxiv.org/abs/1605.00072