A note on the hypergeometric datum $\big((\frac{1}{2},\frac{1}{6},\frac{5}{6}),(1,1)\big)$ and symmetric squares of elliptic curves

TL;DR

This paper explores a mod p congruence linking hypergeometric sums to symmetric squares of elliptic curves, providing insights into their arithmetic properties and connections.

Contribution

It presents an expository analysis of a specific hypergeometric datum and its relation to symmetric squares of elliptic curves, highlighting new congruences.

Findings

Establishes a mod p congruence between hypergeometric sums and elliptic curve symmetric squares.

Provides a detailed exposition on the arithmetic properties of the hypergeometric datum.

Connects hypergeometric sums to elliptic curve theory in a novel way.

Abstract

This is an expository note on a mod $p$ congruence relating the truncated hypergeometric sums associated to $\big((\frac{1}{2},\frac{1}{6},\frac{5}{6}),(1,1)\big)$ to symmetric squares of elliptic curves.