5 citations · 11 across the 10 of their papers we have counts for
10 papers
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…