# Supercongruences arising from hypergeometric series identities

**Authors:** Ji-Cai Liu

arXiv: 1812.09101 · 2018-12-24

## TL;DR

This paper proves two supercongruences involving hypergeometric series, one linked to a Calabi--Yau threefold and the other as a p-adic analogue of Ramanujan's identity, advancing understanding of hypergeometric supercongruences.

## Contribution

It introduces new supercongruences derived from hypergeometric series identities, connecting them to geometric and p-adic contexts.

## Key findings

- Proved a supercongruence related to a modular Calabi--Yau threefold.
- Established a p-adic analogue of Ramanujan's hypergeometric identity.

## Abstract

By using some hypergeometric series identities, we prove two supercongruences on truncated hypergeometric series, one of which is related to a modular Calabi--Yau threefold, and the other is regarded as $p$-adic analogue of an identity due to Ramanujan.

## Full text

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## References

16 references — full list in the complete paper: https://tomesphere.com/paper/1812.09101/full.md

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Source: https://tomesphere.com/paper/1812.09101