1 citations · 2 across the 5 of their papers we have counts for
9 papers
On moments of the Erdős--Hooley Delta-function
R. de la Bretèche, G. Tenenbaum
For integer and real , let . The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\…
On the gap distribution of prime factors
Régis de la Bretèche, Gérald Tenenbaum
Let denote the increasing sequence of distinct prime factors of an integer . For , let denote the number of those indexes su…
Exponential sums with multiplicative coefficients and applications
Régis de la Bretèche, Andrew Granville
We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is "pretentious". This leads to applications in the circle…
On a conjecture of Montgomery and Soundararajan
Régis de la Bretèche, Daniel Fiorilli
We establish lower bounds for all weighted even moments of primes up to in intervals which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds hold u…
On the number of products which form perfect powers and discriminants of multiquadratic extensions
Régis de la Bretèche, Pär Kurlberg, Igor E. Shparlinski
We study some counting questions concerning products of positive integers which form a non-zero perfect square, or more generally, a perfect -th power. We obt…
Minimizing GCD sums and applications to non-vanishing of theta functions and to Burgess' inequality
Régis de la Bretèche, Marc Munsch
In recent years the question of maximizing GCD sums regained interest due to its firm link with large values of -functions. In the present paper we initiate the study of minimiz…