We present new estimates for sums of the divisor function and other similar arithmetic functions in short intervals over function fields. (When the intervals are long, one obtains a good estimate from the Riemann hypothesis.) We obtain an estimate that approaches square-root cancellation as long as the characteristic of the finite field is relatively large. This is done by a geometric method, inspired by work of Hast and Matei, where we calculate the singular locus of a variety whose -points control this sum. This has applications to highly unbalanced moments of L-functions.
"Square-root cancellation for sums of factorization functions over short intervals in function fields." Duke Math. J. 170 (5) 997 - 1026, 1 April 2021. https://doi.org/10.1215/00127094-2020-0060