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 [Formula: see text], for every [Formula: see text], and almost every prime [Formula: see text] in [Formula: see text], the number of primes from the interval [Formula: see text] that are values of [Formula: see text] modulo [Formula: see text] is the expected one, provided [Formula: see text] is not more than [Formula: see text]. We obtain this via a variant of the classical truncated Perron’s formula for the partial sums of the coefficients of a Dirichlet series.

Mellin Convolution and its Extensions, Perron Formula and Explicit Formulae

In this paper we use the Mellin convolution theorem, which is related to Perron's formula. Also we introduce new explicit formulae for arithmetic function which generalize the explicit formulae of Weil for other arithmetic functions different from the Von-Mangoldt function.