Étienne Fouvry

Short sums of the M\"obius function over function fields

We develop a new method which allows us to estimate, with a power saving, sums of the M{\"o}bius function over function fields $\F_p(X)$. The sums run over monic polynomials with all other coefficients in short intervals, of length below the P\'olya--Vinogradov threshold $p^{1/2}$. A classical result of L.~Stickelberge...