Supercongruences for truncated _{𝑛+1}𝐹_{𝑛} hypergeometric series with applications to certain weight three newforms

Mortenson, Eric

doi:10.1090/S0002-9939-04-07697-X

Supercongruences for truncated ${}_{n+1}F_{n}$ hypergeometric series with applications to certain weight three newforms
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by Eric Mortenson

Proc. Amer. Math. Soc. 133 (2005), 321-330

DOI: https://doi.org/10.1090/S0002-9939-04-07697-X

Published electronically: September 20, 2004

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Abstract:

We prove general results on supercongruences between values of truncated $_{n+1}F_{n}$ hypergeometric functions and their character analogs. As a consequence of the main results of this paper, we prove Beukers-type supercongruences for certain weight three newforms.

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