Occasion: SIAM Conference on Applied Algebraic Geometry, Minisymposium on Symbolic Combinatorics
Place: Georgia Tech
We prove a supercongruence modulo \(p^3\) between the \(p\)th Fourier coefficient of a weight 6 modular form and a truncated \(_6F_5\)-hypergeometric series. Novel ingredients in the proof are the comparison of two rational approximations to \(\zeta(3)\) to produce non-trivial harmonic sum identities and the reduction of the resulting congruences between harmonic sums via a congruence between the Apéry numbers and another Apéry-like sequence. We will highlight the role of computer algebra in this work, and give explicit examples indicating the need for algorithmic approaches to certifying \(A \equiv B\).
|2017congruences6f5-ag17.pdf||396.89 KB||Slides (PDF, 39 pages)||12|