Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).
@article{bwmeta1.element.doi-10_1515_math-2016-0067,
author = {Tao Yan Zhao and Lily J. Jin and C. Gu},
title = {Some congruences for 3-component multipartitions},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {783-788},
zbl = {1353.11102},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0067}
}
Tao Yan Zhao; Lily J. Jin; C. Gu. Some congruences for 3-component multipartitions. Open Mathematics, Tome 14 (2016) pp. 783-788. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0067/