The number of irreducible polynomials over finite fields with vanishing trace and reciprocal trace

Yağmur Çakıroğlu, Oğuz Yayla, Emrah Sercan Yılmaz

We present the formula for the number of monic irreducible polynomials of degree $n$ over the finite field ${\mathbb{F}}_q$ where the coefficients of $x^{n-1}$ and $x$ vanish for $n\g…