9 papers
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…