A further look at the overpartition function modulo \(2^4\) and \(2^5\) (Q6631610)

The paper presents a significant contribution to the theory of overpartitions by providing a systematic approach to derive exact generating functions for \(\overline{p}(2n)\), \(\overline{p}(4n)\), \(\overline{p}(8n)\), \(\overline{p}(16n)\), etc., where \(\overline{p}(n)\) denotes the number of overpartitions of \(n\). The authors further establish new infinite families of congruences modulo \(2^4\) and \(2^5\) for \(\overline{p}(n)\). These results extend the existing knowledge of arithmetic properties of overpartition functions and enrich the combinatorial and modular structure of such partitions.