Abstract
Let \(\alpha \) and \(\beta \) be two nonnegative integers such that \(\beta < \alpha \). For an arbitrary sequence \(\{a_n\}_{n\geqslant 1}\) of complex numbers, we investigate linear combinations of the form \(\sum _{k\geqslant 1} S(\alpha k-\beta ,n) a_k\), where S(k, n) is the total number of k’s in all the partitions of n into parts not congruent to 2 modulo 4. The general nature of the numbers \(a_n\) allows us to provide new connections between partitions and functions from multiplicative number theory.
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Merca, M. (2021). A Theta Identity of Gauss Connecting Functions from Additive and Multiplicative Number Theory. In: Bostan, A., Raschel, K. (eds) Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019. Springer Proceedings in Mathematics & Statistics, vol 373. Springer, Cham. https://doi.org/10.1007/978-3-030-84304-5_9
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