Tapani Matala-aho

activity

20162026

collaborators

9 papers

math.NT2026

Simultaneous approximation to pairs of real numbers

Tapani Matala-aho

Let $B_{m}$ and $D_{n}$ be the denominators of the $m$ th and $n$ th convergent of the real numbers $α$ and $β$ , respectively. We introduce an abnormal method in the theory of simult…

math.NT2023

Explicit estimates for the sum $\sum_{k = 0}^{n} k! (k n)^{2} (- 1)^{k}$

Anne-Maria Ernvall-Hytönen, Tapani Matala-aho

We are interested in finding an explicit estimate to the binomial sum $Q_{n} (x) = \sum_{k = 0}^{n} k! (k n)^{2} (- x)^{k}$ at $x = 1$ for $n = 0, 1, 2, \dots$ . Despite of its own interest…

math.NT2022

An analogue of Siegel's determinant

Tapani Matala-aho

Siegel-Shidlovskii theory of $E$ -functions involves a non-vanishing proof for the determinants attached to the linear forms $D^{k} R (t)$ , derivatives of an auxiliary function $R (t)$ .…

math.NT2021

Euler's factorial series, Hardy integral, and continued fractions

Anne-Maria Ernvall-Hytönen, Tapani Matala-Aho, Louna Seppälä

We study $p$ -adic Euler's series $E_{p} (t) = \sum_{k = 0}^{\infty} k! t^{k}$ at a point $p^{a}$ , $a \in Z_{\geq 1}$ , and use Padé approximations to prove a lower bound for the $p$ -ad…

math.NT2018

Euler's divergent series in arithmetic progressions

Anne-Maria Ernvall-Hytönen, Tapani Matala-aho, Louna Seppälä

Let $ξ$ and $m$ be integers satisfying $ξ \neq = 0$ and $m \geq 3$ . We show that for any given integers $a$ and $b$ , $b \neq = 0$ , there are $\frac{φ ( m )}{2}$ reduced residue classes modulo…

math.NT2018

Hermite-Thue equation: Padé approximations and Siegel's lemma

Tapani Matala-aho, Louna Seppälä

Padé approximations and Siegel's lemma are widely used tools in Diophantine approximation theory. This work has evolved from the attempts to improve Baker-type linear independence…

Simultaneous approximation to pairs of real numbers

Explicit estimates for the sum ∑k=0n​k!(kn​)2(−1)k

An analogue of Siegel's determinant

Euler's factorial series, Hardy integral, and continued fractions

Euler's divergent series in arithmetic progressions

Hermite-Thue equation: Padé approximations and Siegel's lemma

Explicit estimates for the sum $\sum_{k = 0}^{n} k! (k n)^{2} (- 1)^{k}$