Tapani Matala-aho

activity

20132026

most citedEuler's factorial series and global relations

18 citations · 31 across the 12 of their papers we have counts for

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13 papers · 1 filter

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★ 5 cited

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★ 1 cited

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…

math.NT2017★ 3 cited

On Mahler's transcendence measure for $e$

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

We present a completely explicit transcendence measure for $e$ . This is a continuation and an improvement to the works of Borel, Mahler and Hata on the topic. Furthermore, we also…

math.NT2017★ 18 cited

Euler's factorial series and global relations

Tapani Matala-aho, Wadim Zudilin

Using Padé approximations to the series $E (z) = \sum_{k = 0}^{\infty} k! (- z)^{k}$ , we address arithmetic and analytical questions related to its values in both $p$ -adic and Archimedean val…

math.NT2016

Rational approximations of the exponential function at rational points

Kalle Leppälä, Tapani Matala-aho, Topi Törmä

We give explicit and asymptotic lower bounds for the quantity $∣ e^{s / t} - M / N ∣$ by studying a generalized continued fraction expansion of $e^{s / t}$ . In cases $∣ s ∣ \geq 3$ we improve e…

math.NT2014★ 1 cited

On approximation measures of $q$ -exponential function

Leena Leinonen, Marko Leinonen, Tapani Matala-aho

We shall present effective approximations measures for certain infinite products related to $q$ -exponential function. There are two main targets. First we shall prove an explicit i…

math.NT2014

On irrationality exponents of generalized continued fractions

Jaroslav Hancl, Kalle Leppälä, Tapani Matala-aho +1

We study how the asymptotic irrationality exponent of a given generalized continued fraction \[ \K_{n=1}^\infty \frac{a_n}{b_n}\,,\quad a_n, b_n\in \mathbb{Z}^+, \] behaves as a fu…

math.NT2013

An explicit Baker type lower bound of exponential values

Anne-Maria Ernvall-Hytönen, Kalle Leppälä, Tapani Matala-aho

Let $I$ denote an imaginary quadratic field or the field $Q$ of rational numbers and $Z_{I}$ its ring of intergers. We shall prove an explicit B…

math.NT2013★ 3 cited

On Baker type lower bounds for linear forms

Tapani Matala-aho

A criterion is given for studying (explicit) Baker type lower bounds of linear forms in numbers $1, Θ_{1}, ..., Θ_{m} \in C^{*}$ over the ring $Z_{I}$ of an imagina…

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

On Mahler's transcendence measure for e

Euler's factorial series and global relations

Rational approximations of the exponential function at rational points

On approximation measures of q-exponential function

On irrationality exponents of generalized continued fractions

An explicit Baker type lower bound of exponential values

On Baker type lower bounds for linear forms

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

On Mahler's transcendence measure for $e$

On approximation measures of $q$ -exponential function