Explicit congruences modulo 2048 for overpartitions
An overpartition of \(n\) is a partition of \(n\) where the first occurrence of each distinct part may be overlined. The number of such overpartitions of \(n\) is denoted by \(\bar p(n)\), Finding congruences modulo powers of primes for overpartitions (as well as other partition functions) is an important field of study in the area. In this paper, the authors find several interesting congruences modulo \(2^{11}\) for \(\bar p(n)\). For instance they show as a special case of Theorem 1.4, that the congruence \[ \bar p(455(2n+1)^2)\equiv 0\pmod{2^{11}} \] holds for all \(n\geq 0\).
scientific article; zbMATH DE number 7345298
scientific article