Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Bordellès, Olivier"'
Autor:
Bordellès, Olivier
We prove a totally explicit bound for short sums of certain non-negative arithmetic functions satisfying a general growth condition, and apply this result to derive two explicit estimates for the Erd\H{o}s-Hooley $\Delta$-function in short intervals.
Externí odkaz:
http://arxiv.org/abs/2402.12333
We investigate various sparse sets that satisfy the prime number theorem. The sparsest of these sets, $\{\lfloor x/n^t \rfloor:n \le x\}$, has density approaching $1/x$ as $t$ approaches infinity.
Externí odkaz:
http://arxiv.org/abs/2304.08736
Autor:
Bordellès, Olivier, Tóth, László
In this note, we extend to a composite modulo a recent result of Chan (2016) dealing with mean values of the product of an integer and its multiplicative inverse modulo a prime number.
Comment: 8 pages. Comments and suggestions are welcome
Comment: 8 pages. Comments and suggestions are welcome
Externí odkaz:
http://arxiv.org/abs/2304.03972
Autor:
Bordellès, Olivier
In this note, we provide an explicit upper bound for $h_K \mathcal{R}_K d_K^{-1/2}$ which depends on an effective constant in the error term of the Ideal Theorem.
Comment: 7 pages. Comments are welcome
Comment: 7 pages. Comments are welcome
Externí odkaz:
http://arxiv.org/abs/2207.11763
Autor:
Bordellès, Olivier, Tóth, László
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.
Comment: 19 pages; c
Comment: 19 pages; c
Externí odkaz:
http://arxiv.org/abs/2112.13409
Publikováno v:
In Journal of Number Theory June 2024 259:93-111
Autor:
Bordellès, Olivier, Tóth, László
Publikováno v:
Lithuanian Math. J. 62 (2022), no. 2, 150-169
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
Externí odkaz:
http://arxiv.org/abs/2104.07443
Autor:
Bordellès, 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:
http://arxiv.org/abs/2009.05751
Autor:
Bordellès, Olivier
This paper is a corrigendum to the article 'On the ideal theorem for number fields`. The main result of this paper proves to be untrue and is replaced by an estimate of a weighted sum with an improved error term.
Externí odkaz:
http://arxiv.org/abs/2006.13667
Autor:
Bordellès, 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
Externí odkaz:
http://arxiv.org/abs/1910.14633