All Questions
5
questions
3
votes
1
answer
406
views
Computing the Hardy-Ramanujan asymptotic formula using method of steepest descent/saddle point method
I am trying to obtain and prove the Hardy-Ramanujan asymptotic approximation formula given by:
$$p(n) \sim \frac{1}{4n\sqrt{3}}e^{\pi\sqrt{\frac{2n}{3}}},$$
by using Dedekind's eta function
$$\eta(z)=...
4
votes
1
answer
199
views
How analytic continuation allows for proof of these 2 theorems in theory of Partitions
Consider these 2 theorems in textbook apsotol introduction to analytic number theory.
1st is generating functions for partitions
I have self studied text and need help in verifying the argument of ...
user775699
3
votes
1
answer
81
views
In how many ways can I express a positive integer as a sum of elements in a subset of $\mathbb Z^+$?
Let $S\subseteq \mathbb Z^+$ be set of positive integers. Given $n\in\mathbb Z^+$, how can I find the number of ways in which we can express $n$ as a sum of elements in $S$? ($S$ can be infinite.)
$$
...
- 7,534
6
votes
1
answer
318
views
Text about connections between complex analysis and partition theory?
I hope this is enough about maths to ask here. As part of my degree I need to do a project consisting of a 7,000-word report on some area of maths (quite a general guideline). I've noticed in studying ...
- 727
1
vote
2
answers
355
views
Proving the Hardy-Ramanujan-Rademacher series for $p(n)$
How to prove the series of the Hardy-Ramanujan-Rademacher for the partition for an integer n using the Cauchy residue theorem?
- 189