Asymptotic Density and the Asymptotics of Partition Functions |
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| Authors: | M B Nathanson |
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| Institution: | (1) School of Mathematics Institute for Advanced Study, Princeton, NJ, 08540, U.S.A. |
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| Abstract: | Let A be a set of positive integers with gcd (A) = 1, and let p
A
(n) be the partition function of A. Let c
0 =   2/3. If A has lower asymptotic density  and upper asymptotic density  , then lim inf log p
A
(n)/c
0 n  and lim sup log p
A
(n)/c
0 n  . In particular, if A has asymptotic density > 0, then log p
A
(n)  c0n. Conversely, if > 0 and log p
A
(n) c
0 n, then the set A has asymptotic density . |
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| Keywords: | |
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