A note on the \(d\)th power residue symbol of \(\mathbb F_q[t]\)
\textit{S. Wright} [J. Number Theory 128, No. 4, 918--925 (2008; Zbl 1167.11006)] found a necessary and sufficient criterion for any nonempty set \(S\) to have the following property: for any fixed nonnegative integer \(q\), there exist infinitely many primes \(p\) such that \(S\) contains exactly \(q\) quadratic residues modulo \(p\). His criterion is expressed by means of a purely combinatorial condition on the prime factors of the elements of \(S\) of odd multiplicity. In this paper the author generalizes Wright's result to \(d\)th power residue symbols for polynomial rings over finite fields.
scientific article; zbMATH DE number 5368236