5 citations · 11 across the 10 of their papers we have counts for
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-unit equation in two variables and Padé approximations
Noriko Hirata-Kohno, Makoto Kawashima, Anthony Poëls +1
In this article, we use Padé approximations constructed for binomial functions, to give a new upper bound for the number of the solutions of the -unit equation. Combining explic…
Generalized hypergeometric -functions take linear independent values
Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima
In this article, we show a new general linear independence criterion related to values of -functions, including the linear independence of values at algebraic points of contiguo…
Padé approximation for a class of hypergeometric functions and parametric geometry of numbers
Makoto Kawashima, Anthony Poëls
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, bi…
Linear independence criteria for generalized polylogarithms with distinct shifts
Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima
For a given rational number and an integer , let us consider a generalized polylogarithmic function, often called the Lerch function, defined by $$Φ_{s}(x,z)= \sum_{k=…