Proves A_mp^mix ≡ A_m^mix mod p^4 for split primes p≥7 p≡1 mod 3 at mixed CM point (1/6,1/3;1), exceeding Hodge-gap prediction via CM enhancement, with inert-prime obstruction.
Hypergeometric supercongruences
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abstract
We discuss two related principles for hypergeometric supercongrences, one related to accelerated convergence and the other to the vanishing of Hodge numbers. This is an extended abstract of a talk given at the workshop "Hypergeometric motives and Calabi-Yau differential equations" at the Mathematical Research Institute (MATRIX) of The University of Melbourne in Creswick, Australia in January of 2017.
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Split-prime supercongruence at the mixed CM point (1/6, 1/3; 1)
Proves A_mp^mix ≡ A_m^mix mod p^4 for split primes p≥7 p≡1 mod 3 at mixed CM point (1/6,1/3;1), exceeding Hodge-gap prediction via CM enhancement, with inert-prime obstruction.