Omega bound for the Piltz divisor problem

Abstract

We obtain improved omega bounds for the error term in the Piltz divisor problem over number fields. Our proof combines Lamzouri's resonance argument with a counting theorem for nonnegative multiplicative functions. The counting theorem gives the estimates needed for the divisor coefficients over a number field and allows us to remove the factor involving the third iterated logarithm from the earlier bounds.

arXiv comment13 pages. Comments and suggestions are welcome