Abstract
Recently, Soon-Yi Kang conjectures that the sign of a certain arithmetic function \(N_{(6)} (n)\) is alternating. We prove her conjecture by employing the circle method and find a positivity result on certain weighted sum of partition functions as an application.
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The authors are grateful to the anonymous referee for his or her careful reading and numerous suggestions which greatly improved the exposition of this paper.
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This research was supported by the Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF2011-0009199).
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Kim, B., Nam, H. On a conjecture of Soon-Yi Kang on a certain partition rank difference. Ramanujan J 35, 467–477 (2014). https://doi.org/10.1007/s11139-014-9561-z
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DOI: https://doi.org/10.1007/s11139-014-9561-z