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- W2963181106 abstract "Let $${overline p _3}left( n right)$$ be the number of overpartition triples of n. By elementary series manipulations, we establish some congruences for $${overline p _3}left( n right)$$ modulo small powers of 2, such as $${overline p _3}left( {16n + 14} right) equiv 0left( {bmod 32} right),{overline p _3}left( {8n + 7} right) equiv 0left( {bmod 64} right)$$ . We also find many arithmetic properties for $${overline p _3}left( n right)$$ modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences: for any integers α ≥ 1 and n ≥ 0, we $$bar p_3 left( {3^{2alpha + 1} left( {3n + 2} right)} right) equiv 0left( {bmod 9cdot2^4 } right),bar p_3 left( {4^{2alpha - 1} left( {56n + 49} right)} right) equiv 0left( {bmod 7} right),bar p_3 left( {7^{2alpha + 1} left( {7n + 3} right)} right) equiv bar p_3 left( {7^{2alpha + 1} left( {7n + 5} right)} right) equiv bar p_3 left( {7^{2alpha + 1} left( {7n + 6} right)} right) equiv 0left( {bmod 7} right)$$ , and for r ∈ {1, 2, 3, 4, 5, 6}, $${overline p _3}left( {11 cdot {7^{4alpha - 1}}left( {7n + r} right)} right) equiv 0left( {bmod 11} right)$$ ." @default.
- W2963181106 created "2019-07-30" @default.
- W2963181106 creator A5082378791 @default.
- W2963181106 date "2016-07-12" @default.
- W2963181106 modified "2023-10-07" @default.
- W2963181106 title "Arithmetic properties of overpartition triples" @default.
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- W2963181106 doi "https://doi.org/10.1007/s10114-016-5673-2" @default.
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