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- W4300455589 abstract "We prove new variants of the Lambert series factorization theorems studied by Merca and Schmidt (2017) which correspond to a more general class of Lambert series expansions of the form $L_a(alpha, beta, q) := sum_{n geq 1} a_n q^{alpha n-beta} / (1-q^{alpha n-beta})$ for integers $alpha, beta$ defined such that $alpha geq 1$ and $0 leq beta < alpha$. Applications of the new results in the article are given to restricted divisor sums over several classical special arithmetic functions which define the cases of well-known, so-termed ordinary Lambert series expansions cited in the introduction. We prove several new forms of factorization theorems for Lambert series over a convolution of two arithmetic functions which similarly lead to new applications relating convolutions of special multiplicative functions to partition functions and $n$-fold convolutions of one of the special functions." @default.
- W4300455589 created "2022-10-03" @default.
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- W4300455589 date "2017-12-02" @default.
- W4300455589 modified "2023-09-27" @default.
- W4300455589 title "Factorization Theorems for Generalized Lambert Series and Applications" @default.
- W4300455589 doi "https://doi.org/10.48550/arxiv.1712.00611" @default.
- W4300455589 hasPublicationYear "2017" @default.
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