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3 votes

Transcendence on $ \alpha+f(\alpha), \alpha f(\alpha) $ and $ \alpha/f(\alpha) $ where $ \al...

Last time I checked, the entire function $f \colon \mathbf C \to \mathbf C \colon z \mapsto a\exp(iz)$ was transcendental for every non-zero $a \in \mathbf C$. So, taking $\alpha = -a = 2\pi$ yields …
Salvo Tringali's user avatar
0 votes
0 answers
234 views

On the irrationality measure of generalized Stoneham numbers

Pick non-zero integers $a,b,c$ with $a,b \ge 2$ and let $\xi_{a,b,c}$ be the sum of the series $\sum_{n=1}^\infty a^{-b^n} c^{-n}$ (no restriction is made on the sign of $c$); when $b = c$ and $\gcd(a …
Salvo Tringali's user avatar
8 votes
1 answer
615 views

On the irrationality measure of $\sum_{n=1}^\infty a^{-b^n}$

Pick integers $a, b \ge 2$ and let $\xi_{a,b}$ be the sum of the series $\sum_{n=1}^\infty a^{-b^n}$. It is known that $\xi_{2,2}$ is transcendental: I learned a proof of this from notes by M. Filaset …
Salvo Tringali's user avatar