Variant of the truncated Perron formula and primes in polynomial sets.

We show under the Generalized Riemann Hypothesis that for every non-constant integer-valued polynomial f , for every δ > 0 , and almost every prime q in [ Q , 2 Q ] , the number of primes from the interval [ x , x + x 1 2 + δ ] that are values of f modulo  q is the expected one, provided Q is not more than x 2 3 − 𝜖 . We obtain this via a variant of the classical truncated Perron's formula for the partial sums of the coefficients of a Dirichlet series. [ABSTRACT FROM AUTHOR]