Partitions into Primes
نویسندگان
چکیده
We investigate the asymptotic behavior of the partition function pΛ(n) defined by ∑∞ n=0 pΛ(n)x n = ∏∞ m=1(1−x), where Λ(n) denotes the von Mangoldt function. Improving a result of Richmond, we show that log pΛ(n) = 2 √ ζ(2)n+O( √ n exp{−c(logn)(log2 n)(log3 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 O(n1/4) if and only if the Riemann Hypothesis holds.
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