Hypergeometric supercongruences.(English)Zbl 1443.11022

Wood, David R. (ed.) et al., 2017 MATRIX annals. Cham: Springer. MATRIX Book Ser. 2, 435-439 (2019).
Summary: We discuss two related principles for hypergeometric supercongruences, one related to accelerated convergence and the other to the vanishing of Hodge numbers.
For the entire collection see [Zbl 1411.37003].

MSC:

 11B65 Binomial coefficients; factorials; $$q$$-identities 11F33 Congruences for modular and $$p$$-adic modular forms 33C20 Generalized hypergeometric series, $${}_pF_q$$

Magma; LMFDB
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References:

 [1] Bosma, W., Cannon, J.J., Fieker, C., Steel, A. (eds.): Handbook of Magma Functions, 2.19 edn., 5291 pp. (2013) [2] Dwork, B.: p-adic cycles. Publ. Math. de l’IHÉS 37, 27-115 (1969) · Zbl 0284.14008 [3] Frechette, S., Ono, K., Papanikolas, M.: Gaussian hypergeometric functions and traces of Hecke operators. Int. Math. Res. Not. 2004(60), 3233-3262 (2004) · Zbl 1088.11029 [4] LMFDB Collaboration: The L-functions and modular forms database (2017). http://www.lmfdb.org [5] Long, L., Tu, F.-T., Yui, N., Zudilin, W.: Supercongruences for rigid hypergeometric Calabi-Yau threefolds. arXiv:1705.01663v1 · Zbl 1443.11053 [6] McCarthy, D.: On a supercongruence conjecture of Rodriguez-Villegas. Proc. Am. Math. Soc. 140, 2241-2254 (2012) · Zbl 1354.11030 [7] Osburn, R., Straub, A., Zudilin, W.: A modular supercongruence for_6F_5: an Apéry-like story. arXiv:1701.04098v1 · Zbl 1429.11039 [8] Rodriguez Villegas, F.: Hypergeometric families of Calabi-Yau manifolds. In: Calabi-Yau Varieties and Mirror Symmetry (Toronto, ON, 2001), pp. 223-231. Fields Institute Communications, vol. 38. American Mathematical Society, Providence (2003) · Zbl 1062.11038 [9] Schoen, C.: On the geometry of a special determinantal hypersurface associated to the Mumford-Horrocks vector bundle. J. Reine Angew. Math. 364, 85-111 (1986) · Zbl 0568.14022
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