28 citations · 82 across the 19 of their papers we have counts for
22 papers
Mean values of arithmetic functions and application to sums of powers
Régis de la Bretèche, Gérald Tenenbaum
We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hoo…
Note on the mean value of the Erdős--Hooley Delta-function
Régis de la Bretèche, Gérald Tenenbaum
For integer and real , let . The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\…
Friable averages of complex arithmetic functions
Régis de la Bretèche, Gérald Tenenbaum
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some complex power of the Riemann zeta function. We obtain asymptotic expansion…
Moments in the Chebotarev density theorem: general class functions
Régis de La Bretèche, Daniel Fiorilli, Florent Jouve
In this paper we find lower bounds on higher moments of the error term in the Chebotarev density theorem. Inspired by the work of Bella\''ıche, we consider general class functions…
Moments in the Chebotarev density theorem: non-Gaussian families
Régis de La Bretèche, Daniel Fiorilli, Florent Jouve
In this paper we investigate higher moments attached to the Chebotarev Density Theorem. Our focus is on the impact that peculiar Galois group structures have on the limiting distri…
Note on a conjecture of Hildebrand regarding friable integers
Régis de la Bretèche, Gérald Tenenbaum
Hildebrand proved that the smooth approximation for the number of -friable integers not exceeding holds for under the Riemann hypothesi…
Friable averages of oscillating multiplicative functions
Régis de la Bretèche, Gérald Tenenbaum
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some negative power of the Riemann zeta function. We obtain asymptotic expansio…
Remarks on the Selberg--Delange method
Régis de la Bretèche, Gérald Tenenbaum
Let be a complex number and let be a multiplicative arithmetic function whose Dirichlet series takes the form , where is associated to a multip…
Moments of moments of primes in arithmetic progressions
Régis de la Bretèche, Daniel Fiorilli
We establish unconditional -results for all weighted even moments of primes in arithmetic progressions. We also study the moments of these moments and establish lower bounds und…
Sommes de Gál et applications
Régis de la Bretèche, Gérald Tenenbaum
We evaluate the asymptotic size of various sums of Gál type, in particular where is a finite s…
On a certain non-split cubic surface
Régis de la Bretèche, Kevin Destagnol, Jianya Liu +2
In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface with a power-savin…
Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables
Régis de la Bretèche, Sary Drappeau
We obtain new estimates on the level of distribution of the set where is irreducible quadratic, for well-factorable moduli, improving a result due t…
Major arcs and moments of arithmetical sequences
Régis de la Bretèche, Daniel Fiorilli
We give estimates for the first two moments of arithmetical sequences in progressions. Instead of using the standard approximation, we work with a generalization of Vaughan's major…
The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves
Régis de la Bretèche, Min Sha, Igor E. Shparlinski +1
We obtain new results concerning the Sato-Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these c…
Counting rational points on the Cayley ruled cubic
Régis de la Bretèche, Tim Browning, Per Salberger
We count rational points of bounded height on the Cayley ruled cubic surface and interpret the result in the context of general conjectures due to Batyrev and Tschinkel.
On Manin's conjecture for a certain singular cubic surface over imaginary quadratic fields
Ulrich Derenthal, Christopher Frei
We prove Manin's conjecture over imaginary quadratic number fields for a cubic surface with a singularity of type E_6.
Density of Châtelet surfaces failing the Hasse principle
R. de la Bretèche, T. D. Browning
Châtelet surfaces provide a rich source of geometrically rational surfaces which do not always satisfy the Hasse principle. Restricting attention to a special class of Châtelet sur…
Binary forms as sums of two squares and Châtelet surfaces
R. de la Bretèche, T. D. Browning
The representation of integral binary forms as sums of two squares is discussed and applied to establish the Manin conjecture for certain Châtelet surfaces defined over the rationa…
On Manin's conjecture for a family of Châtelet surfaces
R. de la Bretèche, T. D. Browning, E. Peyre
The Manin conjecture is established for Châtelet surfaces over Q arising as minimal proper smooth models of the surface Y^2+Z^2=f(X) where f is a totally reducible polynomial of de…
Manin's conjecture for quartic del Pezzo surfaces with a conic fibration
T. D. Browning, R. de la Bretèche
An asymptotic formula is established for the number of rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.
Binary linear forms as sums of two squares
R. de la Breteche, T. D. Browning
We revisit recent work of Heath-Brown on the average order of the quantity r(L_1)r(L_2)r(L_3)r(L_4), for suitable binary linear forms L_1,..., L_4, for integers ranging over quite…
Sums of arithmetic functions over values of binary forms
R. de la Breteche, T. D. Browning
Given a suitable arithmetic function h, we investigate the average order of h as it ranges over the values taken by an integral binary form F. A general upper bound is obtained for…