Abstract
We use the q-binomial theorem, the q-Gauss sum, and the \({}_2\phi _1 \rightarrow {}_2\phi _2\) transformation of Jackson to discover and prove many new weighted partition identities. These identities involve unrestricted partitions, overpartitions, and partitions with distinct even parts. The smallest part of a partition plays an important role in our analysis. This work was motivated in part by the research of Krishna Alladi.
This paper is dedicated to Krishna Alladi on the occasion of his 60th birthday
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Acknowledgements
The authors would like to thank George Andrews for his kind interest, and Jeramiah Hocutt for his careful reading of the manuscript. We are grateful to the anonymous referee for the thoughtful comments and suggestions.
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Berkovich, A., Uncu, A.K. (2017). New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_6
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DOI: https://doi.org/10.1007/978-3-319-68376-8_6
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