$p$-adic formal series and primitive polynomials over finite fields
$p$-adic formal series and primitive polynomials over finite fields
In this paper, we investigate the Hansen-Mullen conjecture with the help of some formal series similar to the Artin-Hasse exponential series over $p$-adic number fields and the estimates of character sums over Galois rings. Given $n$ we prove, for large enough $q$, the Hansen-Mullen conjecture that there exists a primitive …