Distribution of twisted Kloosterman sums modulo prime powers

TL;DR

This paper investigates the distribution of twisted Kloosterman sums modulo prime powers, demonstrating their equidistribution on the real line with respect to a specific measure through elementary calculations.

Contribution

It provides a new elementary proof that twisted Kloosterman sums modulo prime powers are equidistributed, extending understanding of their distribution properties.

Findings

Twisted Kloosterman sums are equidistributed on the real line.

Elementary calculations suffice to establish distribution results.

The sums follow a specific measure on the real line.

Abstract

In this note we study Kloosterman sums twisted by a multiplicative characters modulo a prime power. We show, by an elementary calculation, that these sums become equidistributed on the real line with respect to a suitable measure.