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Arithmetic Properties of Generalized Hypergeometric F -Series
Russian Journal of Mathematical Physics ( IF 1.4 ) Pub Date : 2020-05-31 , DOI: 10.1134/s106192082002003x
V. G. Chirskii

In the paper, using a generalization of the Siegel-Shidlovskii method in the theory of transcendental numbers, we prove the infinite algebraic independence of elements, generated by generalized hypergeometric series, of direct products of the fields of \(\mathbb{K}_v\)-completions of an algebraic number field\(\mathbb{K}\) of finite degree over the field of rational numbers with respect to a valuation v of the field \(\mathbb{K}\) extending the p-adic valuation of the field ℚ over all primes p except for finitely many of them.

中文翻译:

广义超几何F系列的算术性质

在本文中,使用先验数论中的Siegel-Shidlovskii方法的推广,我们证明了由广义超几何级数生成的\(\ mathbb {K} _v场的直接乘积的元素的无限代数独立性\) -关于有理数字段\(\ mathbb {K} \)的估值v的有理数域上有限度的代数数字段\(\ mathbb {K} \)的完成,扩展了p -adic除有限数量的素数外,所有素数p的场field的估值。
更新日期:2020-05-31
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