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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…
math.NT2025
Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution
Arthur Forey, Javier Fresán, Emmanuel Kowalski
We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of…