Statistics of traces of high powers of the Frobenius for biquadratic function fields over finite fields

Abstract

We investigate statistics of trace of high powers of the Frobenius class for biquadratic function fields over finite fields, which generalizes the result of Lorenzo, Meleleo and Milione on the trace of the Frobenius class for biquadratic covers of the projective line. Then we compare our result with Meisner's result on the expected value of high powers of trace of Frobenius of biquadratic curves.