A Large Sieve Inequality for Rational Function Fields Original Research Article

The purpose of this article is to establish an analogue of the Davenport– Halberstam Theorem and a Large Sieve Inequality for rational function fields imageq(t). We then applied our inequality to deduce an analogue of the Brun–Titchmarsch Theorem. We also obtain density zero result on the twin irreducible problem for imageq[t].