In 1949, the Hungarian mathematician István Sándor Gál, then research associate (attaché de recherche) at the CNRS, publishes the demonstration of a conjecture dating back to the 1930s, concerning the maximum size of a quantity of arithmetic nature belonging to a large family whose elements are now called "sums of Gál type". Not until the works of Lewko et Radziwiłł in 2017 was this result specified in the particular case considered by Gál. In a recent work, accepted for publication in the Proceedings of the London Mathematical Society, Regis de la Bretèche and Gérald Tenenbaum get to determine the precise order of magnitude of those sums in another particular case. They deduce remarkable applications, notably concerning notably big values of the Riemann function Zêta on the critical axis.
Régis de la Bretèche is a Professor at Université Paris-Diderot. He is a member of the Institut de mathématiques de Jussieu - Paris Rive Gauche.
Gérald Tenenbaum is a Professor at Université de Lorraine. He is a member of the Institut Elie Cartan de Lorraine.