Irrationality measures for $G\pm5\pi^2/48$ and $L(2,\chi_{-3})$
Building on OpenAI's determinant method for the irrationality of Catalan's constant $G=\sum_{j\ge0}(-1)^j/(2j+1)^2$, we prove \[ \begin{gathered} \mu\Bigl(G-\frac{5\pi^2}{48}\Bigr)\le 38.35,\qquad \mu\Bigl(G+\frac{5\pi^2}{48}\Bigr)\le 38.35,\\ \mu\bigl(L(2,\chi_{-3})\bigr)\le 23.82 , \end{gathered} \] where $\mu$ is the irrationality exponent. We know of no earlier irrationality measure for $G\pm5\pi^2/48$. For $L(2,\chi_{-3})$, which Calegari, Dimitrov and Tang proved irrational, the previous best bound we know of is their effective bound $\mu\le24781$. The approximations come from…
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