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A supercongruence for generalized Domb numbers. (English) Zbl 1337.11001

Summary: Using techniques due to M. Coster [Supercongruences. Ph.D. thesis, Universiteit Leiden (1988)], we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of H. Chan, S. Cooper and F. Sica [Int. J. Number Theory 6, No. 1, 89–97 (2010; Zbl 1303.11009)] and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier’s seven “sporadic” solutions to second order Apéry-like differential equations.

MSC:

11A07 Congruences; primitive roots; residue systems
11F11 Holomorphic modular forms of integral weight

Citations:

Zbl 1303.11009

Software:

OEIS
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Full Text: DOI arXiv Euclid

References:

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