Hilbert's 10th Problem via Mordell curves

Somnath Jha, Debanjana Kundu, Dipramit Majumdar

We show that for $5/6$-th of all primes $p$, Hilbert's 10-th Problem is unsolvable for $\mathbb{Q}({\zeta }_3,\sqrt[3]{p})$. We also show that there is an infinite set $S$ of square free…