Geodesic
On the arithmetic properties of generalized hypergeometric series with irrational parameters
Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1244-1260

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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 $\mathbb{K}$.
Keywords: generalized hypergeometric series, irrational numbers, $p$-adic numbers. 
@article{IM2_2014_78_6_a10,
     author = {V. G. Chirskii},
     title = {On the arithmetic properties of generalized hypergeometric series with irrational parameters},
     journal = {Izvestiya. Mathematics },
     pages = {1244--1260},
     publisher = {mathdoc},
     volume = {78},
     number = {6},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_6_a10/}
}
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V. G. Chirskii. On the arithmetic properties of generalized hypergeometric series with irrational parameters. Izvestiya. Mathematics , Tome 78 (2014) no. 6, pp. 1244-1260. http://geodesic.mathdoc.fr/item/IM2_2014_78_6_a10/