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math.NT2025
On Siegel's problem and Dwork's conjecture for -functions
Javier Fresán, Yeuk Hay Joshua Lam, Yichen Qin
We answer in the negative Siegel's problem for -functions, as formulated by Fischler and Rivoal. Roughly, we prove that there are -functions that cannot be written as polynom…
math.NT2021
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…
math.NT2020★ 12 cited
A non-hypergeometric E-function
Javier Fresán, Peter Jossen
We answer in the negative Siegel's question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential op…