Junnosuke Koizumi

Ap\'ery-type approximations and irrationality measures for certain $q$-series

We construct a three-parameter family of rational approximations to values of $q$-hypergeometric series. Using these approximations, we prove that, for every integer $x$ with $|x|\geq2$, the values at $r=x^{-1}$ of Ramanujan's theta function $\psi(r)=\sum_{n\geq0}r^{n(n+1)/2}$, the generating function $\Delta(r)=\sum_{...