Cancellations Amongst Kloosterman Sums

TL;DR

This paper provides new estimates for bilinear forms involving Kloosterman sums, demonstrating significant cancellations and improving upon recent bounds within specific parameter ranges.

Contribution

It introduces improved bounds for bilinear forms with Kloosterman sums, enhancing understanding of cancellations in short interval parameters.

Findings

Enhanced estimates for bilinear forms with Kloosterman sums

Demonstrated increased cancellations in specific parameter ranges

Improved upon recent results by Blomer et al. and Fouvry et al.

Abstract

We obtain several estimates for bilinear form with Kloosterman sums. Such results can be interpreted as a measure of cancellations amongst with parameters from short intervals. In particular, for certain ranges of parameters we improve some recent results of Blomer, Fouvry, Kowalski, Michel, and Mili\'cevi\'c (2014) and Fouvry, Kowalski and Michel (2014).