2020/11/05 by Ciolan, Alexandru
#11P72 #11P76 #11P82 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2011.02984
In this paper we give a full description of the inequalities that can occur between overpartition ranks. If N(a,c,n) denotes the number of overpartitions of n with rank congruent to a modulo c, we prove that for any c≥7 and 0≤ a<b>N(b,c,n) for n large enough. That the sign of the rank differences N(a,c,n)-N(b,c,n) depends on the residue class of n modulo c in the case of small moduli, such as c=6, is known due to the work of Ji, Zhang and Zhao (2018) and Ciolan (2020). We show that the same behavior holds for c∈\2,3, 4,5\. </b>