Kalle Leppälä

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20132026

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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

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…