K. Srilakshmi | Searcharxiv

arXiv2019

Some congruences for $(s,t)$-regular bipartitions modulo $t$

In this work, we study the function $B_{s,t}(n)$, which counts the number of $(s,t)$-regular bipartitions of $n$. Recently, many authors proved infinite families of congruences modulo $11$ for $B_{3,11}(n)$, modulo $3$ for $B_{3,s}(n)$ and modulo $5$ for $B_{5,s}(n)$. Very recently, Kathiravan proved several infinite families of congruences modulo $11$, $13$ and $17$ for $B_{5,11}(n)$, $B_{5,13}(n)$ and $B_{81,17}(n)$. In this paper, we will prove infinite families of congruences modulo $5$ for $B_{2,15}(n)$, modulo $11$ for $B_{7,11}(n)$, modulo $11$ for $B_{27,11}(n)$ and modulo $17$ for $B_{243,17}(n)$.

math.NT↗

arXiv2019

Some New Congruences for $l$-Regular Partitions Modulo $l$

A partition of $n$ is $l$-regular if none of its parts is divisible by $l$. Let $b_l(n)$ denote the number of $l$-regular partitions of $n$. In this paper, using theta function identities due to Ramanujan, we establish some new infinite families of congruences for $b_l(n)$ modulo $l$, where $l=13,17,23$.

math.NT↗