2025/07/03 by V, Anakha
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2507.02720
Inspired by the recent work by Nadji, Ahmia and Ramírez, we examined the arithmetic properties of Bl1,l2 (n), the number of overpartitions of n whose parts are neither divisible by l1 nor divisible by l2. In particular, we establish some congruences modulo k in 4, 8, 6, 12 satisfied by Bl1,l2 (n) where l1 and l2 take values as arbitrary powers of 2 and 3. Moreover, we extend certain results proved in [26] and [15] for l1 and l2 with random powers of 2 and 3. Generating functions, dissection formulas, and theta functions are used to prove our main findings.