6 papers · 1 filter
On algebraic twists with composite moduli, II
Yongxiao Lin, Philippe Michel
We study bounds for correlation sums of automorphic coefficients on with trace functions of composite moduli. This is a sequel to our previous works wi…
Toroidal families and averages of -functions, II: cubic moments
Ãtienne Fouvry, Emmanuel Kowalski, Philippe Michel +1
Generalizing our previous work on ``toroidal averages'', we study the average of special values of -functions of the form for integers , $…
Bilinear forms with trace functions
Ãtienne Fouvry, Emmanuel Kowalski, Philippe Michel +1
We obtain non-trivial bounds for bilinear sums of trace functions below the Pólya-Vinogradov range assuming only that the geometric monodromy group of the underlying ell-adic shea…
Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums
E. Kowalski, Ph. Michel, W. Sawin
We prove non-trivial bounds for bilinear forms with hyper-Kloosterman sums with characters modulo a prime which, for both variables of length , are non-trivial as soon as $M…
Toroidal families and averages of L-functions, I
Ãtienne Fouvry, Emmanuel Kowalski, Philippe Michel
We initiate the study of certain families of -functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we eva…
The unipotent mixing conjecture
Valentin Blomer, Philippe Michel
We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves.