5 citations · 11 across the 10 of their papers we have counts for
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Rodrigues formula and linear independence for values of hypergeometric functions with parameters vary
Makoto Kawashima
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…
-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=…
Linear Forms in Polylogarithms
Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima
Let be positive integers. Let be a rational number with . Consider the -th Lerch…
Can polylogarithms at algebraic points be linearly independent?
Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima
Let be positive integers. Let be a rational number. Let be the -th Lerch function with $s=1,2,\ldots…
Linear independence of values of logarithms revisited
Makoto Kawashima
Let be an integer, an algebraic number field and with sufficiently small absolute value. In this article, we provide a new lower bound for l…
The digit exchanges in the rotational beta expansions of algebraic numbers
Hajime Kaneko, Makoto Kawashima
In this article, we investigate the -expansions of real algebraic numbers. In particular, we give new lower bounds for the number of digit exchanges in the case where is a P…
Irrationality of special values of formal Laurent series represented by the formal Mellin transform of -functions
Makoto Kawashima
Let be a prime number and the completion of algebraic closure of . Let be an algebraic number field. We fix an embedding $ι_p:\overline{\mathbb…