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- W1509235674 abstract "We investigate the asymptotic behavior of the partition function $p_{Lambda } (n)$ defined by $sum ^{infty }_{n=0}p_{Lambda } (n)x^{n} =prod ^{infty }_{m=1}(1-x^{m})^{-Lambda (m)}$, where $Lambda (n)$ denotes the von Mangoldt function. Improving a result of Richmond, we show that $log p_{Lambda } (n)=2sqrt {zeta (2)n}+O(sqrt nexp {-c(log n) (log _{2} n)^{-2/3}(log _{3} n)^{-1/3}})$, where $c$ is a positive constant and $log _{k}$ denotes the $k$ times iterated logarithm. We also show that the error term can be improved to $O(n^{1/4})$ if and only if the Riemann Hypothesis holds." @default.
- W1509235674 created "2016-06-24" @default.
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- W1509235674 date "2000-02-14" @default.
- W1509235674 modified "2023-09-24" @default.
- W1509235674 title "Partitions into Primes" @default.
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- W1509235674 doi "https://doi.org/10.1090/s0002-9947-00-02386-2" @default.
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