Date: 2017/09/17
Occasion: Palmetto Number Theory Series (PANTS XXVIII)
Place: University of Tennessee
Abstract
We discuss congruences between truncated hypergeometric series and modular forms. Specifically, we discuss a supercongruence modulo \(p^3\) between the \(p\)th Fourier coefficient of a weight 6 modular form and a truncated \(_6F_5\)-hypergeometric series. The story is intimately tied with Apéry's proof of the irrationality of \(\zeta(3)\).
This is joint work with Robert Osburn and Wadim Zudilin.
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| Link | Size | Description | Hits |
|---|---|---|---|
| 2017congruences6f5-pants.pdf | 380.41 KB | Slides (PDF, 33 pages) | 1004 |