Modular Forms and Numerical Explorations of Rational Approximations to $\zeta (3)$

Cynthia Bortolotto, Lucas Oliveira

We revisit Beukers' modular-form proof of the irrationality of $\zeta (3)$ from the point of view of the auxiliary weight two modular form. For the Fricke group ${\Gamma }_0(6{)}^{\star }$, we show…