# Publications and Preprints

Variations of Erd\H{o}s- Selfridge superelliptic curves and their rational points
by
Pranabesh Das, Shanta Laishram and N. Saradha
For the superelliptic curves of the form $$(x+1) \cdots(x+i-1)(x+i+1)\cdots (x+k)=y^\ell$$ with $k \geq 3$ and $\ell \geq 2,$ a prime, for some values of $i$ in the range $2\leq i\leq k,$ we bound $\ell< e^{3^k},$ as in a recent paper of Bennett and Siksek.

isid/ms/2016/14 [fulltext]