All Questions
6
questions
3
votes
2
answers
176
views
Where can I find a proof of the asymptotic expresion of partition numbers by Hardy-Ramanujan?
I'm starting to study number theory and I´m interested in partitions, but I don't find a proof of this asymptotic expression $p(n)$ given by Hardy-Ramanujan.
- 39
2
votes
1
answer
135
views
Integer partition asymptotics for a finite set of relatively prime integers.
I need to get approximations for partition functions in order to limit the expansion of the generating series used to work out the exact value.
The unrestricted partition function $ p(n) $ counts the ...
- 151
1
vote
2
answers
215
views
Is the Hardy-Ramanujan approximation of $p(n)$ an upper bound?
The approximation is usually written as
$$
p(n) \sim \frac{1}{4n\sqrt{3}}e^{\pi\sqrt{\frac{2n}{3}}}
$$
But every graph I've seen makes it look like this is an asymptotic upper bound for $p(n)$. Is ...
- 11
7
votes
1
answer
938
views
Asymptotic behavior of unique integer partitions
Okay, this is one of those questions that I'm sure has a very simple answer I'm missing, and I'd appreciate any push in the right direction.
Consider a very large integer $N$. Stealing an example ...
- 330
3
votes
1
answer
173
views
asymptotic approximation for number of partitions of integer that do contain 1 nor 2
Hardy and Ramanujan provided a famous asymptotic approximation to $P(n)$ the number of partitions of an integer $n$ when $n$ gets large. I wonder if there is an asymptotic approximation to $P_{\...
- 31
10
votes
2
answers
5k
views
Hardy Ramanujan Asymptotic Formula for the Partition Number
I am needing to use the asymptotic formula for the partition number, $p(n)$ (see here for details about partitions).
The asymptotic formula always seems to be written as,
$$ p(n) \sim \frac{1}{4n\sqrt{...
- 4,660