Ramanujan's circular summation, t-cores and twisted partition identities
Date
2019
Authors
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Source Title
Journal of Mathematical Analysis and Applications
Print ISSN
0022-247X
Electronic ISSN
Publisher
Elsevier
Volume
479
Issue
1
Pages
773 - 788
Language
English
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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 discover modular relations among circular summation function partition function and give uniform proof of Ramanujan’s partition congruences for the moduli 5, 7 and 11. We also prove several interesting congruence relations.