Let 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 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 modulo 3. For example, we prove that for n, α ≥ 0, .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-6, author = {Ernest X. W. Xia}, title = {Some new infinite families of congruences modulo 3 for overpartitions into odd parts}, journal = {Colloquium Mathematicae}, volume = {144}, year = {2016}, pages = {255-266}, zbl = {06498817}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm142-2-6} }
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/