Square-root cancellation for sums of factorization functions over short intervals in function fields

We present new estimates for sums of the divisor function and other similar arithmetic functions in short intervals over fields. (When are long, one obtains a good estimate from Riemann hypothesis.) obtain an that approaches square-root cancellation as long characteristic finite field is relatively large. This done by geometric method, inspired work Hast Matei, where we calculate singular locus variety whose Fq-points control this sum. has applications to highly unbalanced moments L-functions.