Étienne Fouvry

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20222026

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math.NT2026

Short sums of the Möbius function over function fields

Etienne Fouvry, Igor E. Shparlinski, Ping Xi

We develop a new method which allows us to estimate, with a power saving, sums of the M{ö}bius function over function fields $F_{p} (X)$ . The sums run over monic polynomials…

math.NT2026

Tridimensional character sums with polynomial arguments and applications

Étienne Fouvry, Igor E. Shparlinski, Ping Xi

Let $p$ be a large prime and $χ$ a non-trivial Dirichlet character modulo $p$ . We study the character sum \[ \sum_{a \sim A} \sum_{b \sim B} \sum_{c \sim C} α(a,b) β(c)χ(f(a) + bc)…