Explicit congruences modulo 2048 for overpartitions
Let \bar{p}(n) p n denote the number of overpartitions of n Recently, a number of congruences modulo powers of 2, 3 and 5 have been discovered. The moduli for these congruences modulo powers of 2 discovered before ranged as high as 1024. In this paper, we establish explicit congruences modulo 2048 for \bar{p}(n) p n In particular, we deduce some strange congruences modulo 2048 for \bar{p}(n) p n For instance, we prove that for $n\ge 0$ n 0 \begin{aligned} \bar{p}(1820n^2+1820n+455)\equiv 0\\pmod {2048} \end{aligned} p 1820 n 2 1820 n 455 0 mod 2048