Bibekananda Maji

Affiliation: IIT Indore

Title Of Talk: Rademacher-type exact formula and higher order Turán inequalities for r-colored l-regular partitions

URLS:
https://arxiv.org/abs/2511.05907

Abstract: In 1937, Rademacher refined the circle method of Hardy and Ramanujan to derive an exact convergent series for the partition function $p(n)$. In 1942, Hua derived an exact formula for the distinct part partition function, and in 1971, Hagis generalized this result to the case of $l$-regular partitions. More recently, Iskander, Jain, and Talvola established a Rademacher-type exact formula for the $r$-colored partition function. In this talk, we shall discuss a Rademacher-type exact formula for $r$-colored $l$-regular partitions for any $r$ and $l\ge 2$. As an application, we derive higher order Turán inequalities for the $r$-colored $l$-regular partition function using a result of Griffin, Ono, Rolen, and Zagier. This is joint work with Archit Agarwal and Meghali Garg.

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