Kloosterman sums over finite Frobenius rings

TL;DR

This paper extends the study of Kloosterman sums to finite commutative Frobenius rings, deriving identities and moment computations that generalize classical results in number theory.

Contribution

It introduces a generalized ring-theoretic framework for Kloosterman sums over Frobenius rings, providing new identities and moment formulas.

Findings

Derived identities for twisted Kloosterman sums

Computed moments of Kloosterman sums in Frobenius rings

Extended classical Kloosterman sum results to a broader algebraic setting

Abstract

We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. We prove a number of identities for twisted Kloosterman sums, loosely clustered around moment computations.