M. Kawashima

activity

20162023

most citedCan polylogarithms at algebraic points be linearly independent?

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

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Showing 2019 · math.NTShow all

3 papers · 2 filters

math.NT2019★ 5 cited

Can polylogarithms at algebraic points be linearly independent?

Sinnou David, Noriko Hirata-Kohno, Makoto Kawashima

Let $r, m$ be positive integers. Let $0 \leq x < 1$ be a rational number. Let $Φ_{s} (x, z)$ be the $s$ -th Lerch function $\sum_{k = 0}^{\infty} \frac{z ^{k + 1}}{( k + x + 1 ) ^{s}}$ with $s=1,2,\ldots…

math.NT2019

Linear independence of values of logarithms revisited

Makoto Kawashima

Let $m \geq 2$ be an integer, $K$ an algebraic number field and $α \in K ∖ {0, - 1}$ with sufficiently small absolute value. In this article, we provide a new lower bound for l…

math.NT2019★ 1 cited

The digit exchanges in the rotational beta expansions of algebraic numbers

Hajime Kaneko, Makoto Kawashima

In this article, we investigate the $β$ -expansions of real algebraic numbers. In particular, we give new lower bounds for the number of digit exchanges in the case where $β$ is a P…