Padé approximation for a class of hypergeometric functions and parametric geometry of numbers

Kawashima, Makoto; Poëls, Anthony

doi:10.1016/j.jnt.2022.05.009

Journal of Number Theory

2023

DOI: 10.1016/j.jnt.2022.05.009

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Padé approximation for a class of hypergeometric functions and parametric geometry of numbers

Makoto Kawashima

Anthony Poëls

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2023

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Cited by 2 publications

References 23 publications

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Rodrigues Formula and Linear Independence for Values of Hypergeometric Functions With Varying Parameters

KAWASHIMA

2023

J. Aust. Math. Soc.

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In this article, we prove a generalized Rodrigues formula for a wide class of holonomic Laurent series, which yields a new linear independence criterion concerning their values at algebraic points. This generalization yields a new construction of Padé approximations including those for Gauss hypergeometric functions. In particular, we obtain a linear independence criterion over a number field concerning values of Gauss hypergeometric functions, allowing the parameters of Gauss hypergeometric functions to vary.

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Rodrigues Formula and Linear Independence for Values of Hypergeometric Functions With Varying Parameters

KAWASHIMA

2023

J. Aust. Math. Soc.

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S-unit equation in two variables and Padé approximations

Hirata‐Kohno

Kawashima

Poëls

et al. 2023

Int. J. Number Theory

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In this paper, we use Padé approximations, constructed in [Kawashima and Poëls, Padé approximations for shifted functions and parametric geometry of numbers, J. Number Theory 243 (2023) 646–687] for binomial functions, to give a new upper bound for the number of the solutions of the [Formula: see text]-unit equation in two variables. Combining explicit Padé approximants with a simple argument relying on Mahler measure as well as the local height, we refine the bound due to Evertse [On equations in [Formula: see text]-units and the Thue-Mahler equation, Invent. Math. 75 (1984) 561–584].

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Padé approximation for a class of hypergeometric functions and parametric geometry of numbers

Cited by 2 publications

References 23 publications

Rodrigues Formula and Linear Independence for Values of Hypergeometric Functions With Varying Parameters

Rodrigues Formula and Linear Independence for Values of Hypergeometric Functions With Varying Parameters

S-unit equation in two variables and Padé approximations

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