Irreducible polynomials in arithmetic progressions and a problem of Szegedy

Lajos Hajdu
2004 Publicationes mathematicae (Debrecen)  
In this paper we show that under certain assumptions, every sufficiently long arithmetic progression of polynomials in Z[x] contains an irreducible polynomial. Our result is effective, and can be considered as an extension of a result of Győry on a problem of Szegedy concerning irreducible polynomials. We also derive a lower bound for the constant C 1 (m) occurring in Szegedy's problem. Finally, we provide some numerical results, and propose a quantitative version of this problem.
doi:10.5486/pmd.2004.3224 fatcat:l4e4kmfqyrhmddxzo6gol73oo4