Value sets of folding polynomials over finite fields

Abstract

Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complexLie algebra g. We find the cardinality of the value sets of the folding polynomials $P_g^k(x)inboldsymbol Zlbrack xrbrack$ of arbitrary rank $ngeq1$ over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.