4 citations · 12 across the 15 of their papers we have counts for
22 papers
On a Smoothed Walfisz Divisor Problem
Olivier Bordellès, Florian Daval
This work is in the spirit of our previous investigation on a smooth Dirichlet divisor problem, where we now replace the Dirichlet divisor function by the sum-of-divisors funct…
A note on the -adic valuation of
Olivier Bordellès
In this note, we obtain an exact formula for the -adic valuation of where is an odd prime, allowing us to derive an explicit upper bound which is asymptotically bet…
On a Smoothed Dirichlet Divisor Problem
Olivier Bordellès, Florian Daval
Hardy showed that $\sum_{n \ioe x}τ(n)-x(\log x +2γ-1)$ is not . In this article, we prove that $\sum_{n \ioe x}τ(n)(1-\frac{x}{n})-xP(\log x)=\frac{1}{4}+O \left( \fra…
An explicit result for short sums of positive arithmetic functions
Olivier Bordellès
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 es…
Mean values of the product of an integer and its modular inverse
Olivier Bordellès, László Tóth
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 num…
Sparse sets that satisfy the prime number theorem
Olivier Bordellès, Randell Heyman, Dion Nikolic
We investigate various sparse sets that satisfy the prime number theorem. The sparsest of these sets, , has density approaching as appr…
From the Ideal Theorem to the class number
Olivier Bordellès
In this note, we provide an explicit upper bound for which depends on an effective constant in the error term of the Ideal Theorem.
Additive arithmetic functions meet the inclusion-exclusion principle, II
Olivier Bordellès, László Tóth
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…
Additive arithmetic functions meet the inclusion-exclusion principle: Asymptotic formulas concerning the GCD and LCM of several integers
Olivier Bordellès, László Tóth
We obtain asymptotic formulas for the sums and involving the gcd and lcm of the i…
On certain sums of number theory
Olivier Bordellès
We study sums of the shape where is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We im…
Corrigendum to the paper 'On the ideal theorem for number fields` [Funct. Approximatio, Comment. Math. 53, No. 1, 31--45 (2015)]
Olivier Bordellès
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…
On restricted divisor sums associated to the Chowla-Walum conjecture
Olivier Bordellès
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…
A Note on a Unitary Analog to Redheffer's Matrix
Olivier Bordellès
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…
Sums of certain fractional parts
Olivier Bordellès
In this note, an upper bound for the sum of fractional parts of certain smooth functions is established. Such sums arise naturally in numerous problems of analytic number theory. T…
On a sum involving the Euler function
Olivier Bordellès, Lixia Dai, Randell Heyman +2
We obtain reasonably tight upper and lower bounds on the sum , involving the Euler functions and the integer…
On some identities in multiplicative number theory
Olivier Bordellès, Benoit Cloitre
Using elementary means, we prove several identities involving the Möbius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
On the error term of a lattice counting problem, II
Olivier Bordellès
Under the Riemann Hypothesis, we improve the error term in the asymptotic formula related to the counting lattice problem studied in a first part of this work. The improvement come…
Denominators of Bernoulli polynomials
Olivier Bordellès, Florian Luca, Pieter Moree +1
For a positive integer let where runs over all primes and is the sum of the base digits of . For all we prove th…
On a conjecture of B. C. Kellner
Olivier Bordellès
The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results…
When the number of divisors is a quadratic residue
Olivier Bordellès
Let be a prime number and define where is the number of divisors of and is the Legendre symbol…
Short interval results for certain prime-independent multiplicative functions
Olivier Bordellès
Using recent results from the theory of integer points close to smooth curves, we give an asymptotic formula for the distribution of values of a class of integer-valued prime-indep…
Short interval results for a class of arithmetic functions
Olivier Bordellès
Using estimates on Hooley's -function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic fun…