Vol. 70, No. 1, pp. 55–63 (2018)

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New congruences for overcubic partition function

C. Shivashankar and M. S. Mahadeva Naika

Department of Mathematics, Reva University, Rukmini Knowledge Park, Yelahanka, Bengaluru – 560 064, Karnataka, India E-mail: shankars224@gmail.com and Department of Mathematics, Bangalore University, Central College Campus, Bangalore – 560 001, Karnataka, India E-mail: msmnaika@rediffmail.com

Abstract: In 2010, Byungchan Kim introduced a new class of partition function a ¯(n), the number of overcubic partitions of n and established a ¯(3n+2)0(mod3). 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(n). We prove a number of results for a ¯(n), for example, for α0 and n0, a ¯(8n+5)0(mod16), a ¯(8n+7) 0(32)32,a(8 32+2n+32+2)3 a(8n+1)(8)8·

Keywords: Overcubic partitions; congruences; theta function.

Classification (MSC2000): 11P83; 05A15, 05A17

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Electronic fulltext finalized on: 16 Dec 2017. This page was last modified: 11 Mai 2018.

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