On the arithmetic properties of generalized hypergeometric series with irrational parameters

We prove the existence of an infinite set of primes $p$ such that the generalized hypergeometric series with irrational parameters in a number field $\mathbb{K}$ is not equal to zero in the algebraic extension $\mathbb{K}_v$ of the field of $p$-adic numbers, where $v$ is an extension of the $p$-adic valuation to $\mathbb{K}$.