Short Sums of Trace Functions in Function Fields

This paper investigates the behavior of trace functions in function fields, aiming for square-root cancellation in short sums. This has implications for problems in analytic number theory over finite fields, such as Mordell's problem and the variance of Kloosterman sums. The work focuses on specific conditions for the trace functions, including squarefree moduli and slope constraints. The function field version of Hooley's Hypothesis R* is a notable special case.