Number Theory SeminarExport this event to calendar

Tuesday, October 2, 2018 — 1:30 PM EDT

Pranabesh Das, Pure Mathematics, University of Waterloo

"Variants of Erd{\H o}s--Selfridge superelliptic curves and their rational points"

For the superelliptic curves of the form \[(x+1) \cdots(x+i-1)(x+i+1)\cdots (x+k)=y^\ell \] with $y \neq 0, k \geq 3$, $\ell \geq 2,$ a prime and for $i \in [2,k] \setminus \Omega$, we show that $\ell< e^{3^k}$. Here $\Omega$ denotes the interval $[p_\theta , (k-p_\theta))$, where $p_{\theta}$ is the least prime $\geq k/2$. Bennett and Siksek obtained similar bound for $i=1$ in a recent paper. This talk is based on a recent joint work with Laishram and Saradha.
Location 
MC 5417


,
Canada

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