Bilinear forms with Kloosterman and Gauss sums in function fields.

In recent years, there has been a lot of progress in obtaining non-trivial bounds for bilinear forms of Kloosterman sums in Z / m Z for arbitrary integers m. These results have been motivated by a wide variety of applications, such as improved asymptotic formulas for moments of L -functions. However, there has been very little work done in this area in the setting of rational function fields over finite fields. We remedy this and provide a number of new non-trivial bounds for bilinear forms of Kloosterman and Gauss sums in this setting, based on new bounds on the number of solutions to certain modular congruences in F q [ T ]. These improve upon some results of Macourt and Shparlinski (2019). [ABSTRACT FROM AUTHOR]