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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.06534 |
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Table of Contents:
- We prove new linear independence results for the values of generalized hypergeometric functions ${}_pF_q$ at several distinct algebraic points, over arbitrary algebraic number fields. Our approach combines constructions of type II Padé approximants with a novel non-vanishing argument for generalized Wronskians of Hermite type. The method applies uniformly across all parameter regimes. Even for $p = q+1$, we extend known results from single-point to multi-point settings over general number fields, in the both complex and $p$-adic settings. When $p < q+1$, we establish linear independence results over arbitrary number fields; and for $p > q+1$, we confirm that the values do not satisfy global linear relations in the $p$-adic setting. Our results generalize and strengthen earlier work by Chudnovsky's, Nesterenko, Sorokin, Delaygue and others, and demonstrate the flexibility of our Padé construction for families of contiguous hypergeometric values.