5 citations · 12 across the 5 of their papers we have counts for
8 papers
Improved bounds for the Fourier uniformity conjecture
Cédric Pilatte
Let denote the Liouville function. We prove that as…
Unconditional correctness of recent quantum algorithms for factoring and computing discrete logarithms
Cédric Pilatte
In 1994, Shor introduced his famous quantum algorithm to factor integers and compute discrete logarithms in polynomial time. In 2023, Regev proposed a multi-dimensional version of…
Improved bounds for the two-point logarithmic Chowla conjecture
Cédric Pilatte
Let be the Liouville function, defined as where is the number of prime factors of with multiplicity. In 2021, Helfgott and Radziwiłł proved tha…
A solution to the Erdős-Sárközy-Sós problem on asymptotic Sidon bases of order 3
Cédric Pilatte
A set is a Sidon set if all pairwise sums (for , ) are distinct. A set is an asymptotic basis of o…
New bound for Roth's theorem with generalized coefficients
Cédric Pilatte
We prove the following conjecture of Shkredov and Solymosi: every subset such that contains…
A note on optimal degree-three spanners of the square lattice
Damien Galant, Cédric Pilatte
In this short note, we prove that the degree-three dilation of the square lattice is . This disproves a conjecture of Dumitrescu and Ghosh. We give a com…
NP-completeness of slope-constrained drawing of complete graphs
Cédric Pilatte
We prove the NP-completeness of the following problem. Given a set of slopes and an integer , is it possible to draw a complete graph on vertices in the plane…
On the sets of points forming directions
Cédric Pilatte
Let be a set of points in the plane, no three of which are collinear. Suppose that determines directions. That is to say, the segments whose endpoints are i…