Kloosterman sums in residue rings
Volume 164 / 2014
Acta Arithmetica 164 (2014), 43-64
MSC: Primary 11L05.
DOI: 10.4064/aa164-1-4
Abstract
We generalize some of our previous results on Kloosterman sums [Izv. Mat., to appear] for prime moduli to general moduli. This requires establishing the corresponding additive properties of the reciprocal-set $ I^{-1}=\{x^{-1}: x\in I\}, $ where $I$ is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun–Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of general moduli.
