We prove an $${{\mathbb {F}}}_p$$ -Selberg integral formula, in which the is element of finite field with odd prime number p elements. The formula motivated by analogy between multidimensional hypergeometric solutions KZ equations and polynomial same reduced modulo p.

We study certain aspects of the Selberg sieve, in particular when sifting by rather thin sets primes. derive new results for lower bound sieve suited especially this setup and we apply them to give a sieve-propelled proof o