Some new infinite families of congruences modulo 3 for overpartitions into odd parts
Ernest X. W. Xia
Colloquium Mathematicae, Tome 144 (2016), p. 255-266 / Harvested from The Polish Digital Mathematics Library

Let p̅o(n) denote the number of overpartitions of n in which only odd parts are used. Some congruences modulo 3 and powers of 2 for the function p̅o(n) have been derived by Hirschhorn and Sellers, and Lovejoy and Osburn. In this paper, employing 2-dissections of certain quotients of theta functions due to Ramanujan, we prove some new infinite families of Ramanujan-type congruences for p̅o(n) modulo 3. For example, we prove that for n, α ≥ 0, p̅o(4α(24n+17))p̅o(4α(24n+23))0(mod3).

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:284139
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     title = {Some new infinite families of congruences modulo 3 for overpartitions into odd parts},
     journal = {Colloquium Mathematicae},
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     year = {2016},
     pages = {255-266},
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Ernest X. W. Xia. Some new infinite families of congruences modulo 3 for overpartitions into odd parts. Colloquium Mathematicae, Tome 144 (2016) pp. 255-266. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-6/