Arithmetic Properties of Generalized Hypergeometric F-Series
- Authors: Chirskii V.G.1
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Affiliations:
- Faculty of Mechanics and Mathematics
- Issue: Vol 98, No 3 (2018)
- Pages: 589-591
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225589
- DOI: https://doi.org/10.1134/S106456241807013X
- ID: 225589
Cite item
Abstract
A generalization of the Siegel–Shidlovskii method in the theory of transcendental numbers is used to prove the infinite algebraic independence of elements (generated by generalized hypergeometric series) of direct products of fields \(\mathbb{K}_v\), which are completions of an algebraic number field \(\mathbb{K}\) of finite degree over the field of rational numbers with respect to valuations v of \(\mathbb{K}\) extending p-adic valuations of the field ℚ over all primes p, except for a finite number of them.
About the authors
V. G. Chirskii
Faculty of Mechanics and Mathematics
Author for correspondence.
Email: vgchirskii@yandex.ru
Russian Federation, Moscow, 119992