5 citations · 7 across the 7 of their papers we have counts for
7 papers
Counting Theorems for Algebraic Relations
Gal Binyamini, Noriko Hirata-Kohno, Makoto Kawashima +1
Let X be a set definable in a sharply o-minimal structure. We consider the problem of counting the number of points where X intersects algebraic varieties V over Q of dimension k <…
Linear independence of values of hypergeometric functions and arithmetic Gevrey series
Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima
We prove new linear independence results for the values of generalized hypergeometric functions at several distinct algebraic points, over suitable algebraic number field…
-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…
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…