collaborators

4 papers

math.NT2026

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…

math.NT2026

Toroidal families and averages of -functions, II: cubic moments

Étienne 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 , $…

math.NT2026

Bilinear forms with trace functions

Étienne 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…

math.NT2025

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…