MATEMATIČKI VESNIK Vol. 70, No. 1, pp. 55–63 (2018) 

New congruences for overcubic partition functionC. Shivashankar and M. S. Mahadeva NaikaDepartment of Mathematics, Reva University, Rukmini Knowledge Park, Yelahanka, Bengaluru – 560 064, Karnataka, India Email: shankars224@gmail.com and Department of Mathematics, Bangalore University, Central College Campus, Bangalore – 560 001, Karnataka, India Email: msmnaika@rediffmail.comAbstract: In 2010, Byungchan Kim introduced a new class of partition function $\overline{a}\left(n\right)$, the number of overcubic partitions of $n$ and established $\overline{a}(3n+2)\equiv 0\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}3)$. Our goal is to consider this function from an arithmetic point of view in the spirit of Ramanujan’s congruences for the unrestricted partition function $p\left(n\right)$. We prove a number of results for $\overline{a}\left(n\right)$, for example, for $\alpha \ge 0$ and $n\ge 0$, $\overline{a}(8n+5)\equiv 0\phantom{\rule{4.44443pt}{0ex}}(mod\phantom{\rule{0.277778em}{0ex}}16)$, Keywords: Overcubic partitions; congruences; theta function. Classification (MSC2000): 11P83; 05A15, 05A17 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Dec 2017. This page was last modified: 11 Mai 2018.
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