Occasion: Palmetto Number Theory Series (PANTS XXVIII)
Place: University of Tennessee
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 \(\zeta(3)\).
|2017congruences6f5-pants.pdf||380.41 KB||Slides (PDF, 33 pages)||132|