16 citations · 21 across the 10 of their papers we have counts for
8 papers · 1 filter
A fourth derivative test for exponential sums
O Robert, P Sargos
We give an upper bound for the exponential in terms of and , where is a small positive number which denotes the size of the fourth derivat…
A mean-value theorem for exponential sums. Applications to Weyl's inequality
Olivier Robert, Patrick Sargos
We study the mean value of sixth power of some exponential sums following an idea due to Bombieri and Iwaniec. The result applies to Weyl's inequality, following an idea due to Hea…
On the sum of two powered numbers
Jörg Brüdern, Olivier Robert
Fix a positive real number . The natural numbers with largest square-free divisor not exceeding form a set , say. It is shown that whenever then a…
On the distribution of powered numbers
Jörg Brüdern, Olivier Robert
Asymptotic formulae are established for the number of natural numbers with largest square-free divisor not exceeding , for any fixed positive parameter $\varthet…
Rational points on an intersection of diagonal forms
Simon Boyer, Olivier Robert
We consider intersections of n diagonal forms of degrees k 1 < < kn, and we prove an asymptotic formula for the number of rational points of bounded h…
On Artin's conjecture: linear slices of diagonal hypersurfaces
Jörg Brüdern, Olivier Robert
Artin's conjecture is established for all forms that can be realised as a diagonal form on an hyperplane.
Zero free regions for Dirichlet series
Christophe Delaunay, Emmanuel Fricain, Elie Mosaki +1
In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for -functions. Our results generaliz…
Small gaps in coefficients of L-functions and B-free numbers in small intervals
Emmanuel Kowalski, Olivier Robert, Jie Wu
We discuss questions related to the non-existence of gaps in the series defining modular forms and other arithmetic functions of various types, and improve results of Serre, Balog…