Chebyshev polynomials and a refinement of the local residue/non-residue structure at a prime

Kok Seng Chua

The basic power function $t_n(x)=x^n$ is in some sense a classical limit for large $x$, of the monictised Chebyshev polynomial of the first kind $T_n(x)/2^{n-1}$. A theorem of Ritt…