# Some congruences for 3-component multipartitions

Tao Yan Zhao; Lily J. Jin; C. Gu

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 783-788
- ISSN: 2391-5455

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topTao Yan Zhao, Lily J. Jin, and C. Gu. "Some congruences for 3-component multipartitions." Open Mathematics 14.1 (2016): 783-788. <http://eudml.org/doc/287119>.

@article{TaoYanZhao2016,

abstract = {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).},

author = {Tao Yan Zhao, Lily J. Jin, C. Gu},

journal = {Open Mathematics},

keywords = {Congruences; Multipartitions; Theta functions; multipartitions; congruences; theta functions},

language = {eng},

number = {1},

pages = {783-788},

title = {Some congruences for 3-component multipartitions},

url = {http://eudml.org/doc/287119},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Tao Yan Zhao

AU - Lily J. Jin

AU - C. Gu

TI - Some congruences for 3-component multipartitions

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 783

EP - 788

AB - 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).

LA - eng

KW - Congruences; Multipartitions; Theta functions; multipartitions; congruences; theta functions

UR - http://eudml.org/doc/287119

ER -

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