论文信息 - Partitions into Primes

Partitions into Primes

We investigate the asymptotic behavior of the partition function PA(n) defined by ??0PA(n)Xn = fJ1 (1-Xm)-A(m), where A(n) denotes the von Mangoldt function. Improving a result of Richmond, we show that logpA(n) = 2( (2)n + O(?nexp{-c(logn)(1og2 n2/3(1og3 n) -1/3}), where c is a positive constant and logk denotes the k times iterated logarithm. We also show that the error term can be improved to 0(n1/4) if and only if the Riemann Hypothesis holds.

Yifan Yang | Yifan Yang

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