Arithmetic properties of polynomial specializations over finite fields

Paul Pollack
2009 Acta Arithmetica  
We present applications of some recent results that establish a partial finite field analogue of Schinzel's Hypothesis H. For example, we prove that the distribution of gaps between degree n prime polynomials over Fp is close to Poisson for p large compared to n. We also estimate the number of polynomial substitutions without prime factors of large degree ("smooth" polynomial substitutions); this confirms a finite field analogue of a conjecture of Martin in certain ranges of the parameters.
more » ... the parameters. Other topics considered include an analogue of Brun's constant for polynomials and "smooth" values of neighboring polynomials.
doi:10.4064/aa136-1-5 fatcat:wb7awmetyncivafkhbbk2ac6ii