Alexander Berkovich, Frank G. Garvan, and Hamza Yesilyurt
Ramanujan's circular summation, t-cores and twisted partition identities, J. Math. Anal. Appl., 479(2019), no. 1, 773-788.

Abstract: In this paper, we give new evaluations for Ramanujan's circular summation function. We also provide simpler proofs for known evaluations and give some generalizations. We prove a simple but elegant identity that relates Ramanujans circular summation funtion $t$-cores and partition function. As applications we give a uniform proof of Ramanujan's partition congruences for the modulus $5$, $7$ and $11$. We also give new proofs for some identities proven by Rademacher.

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