# Questions tagged [circle-method]

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### How to find the right path of integration to get the asymptotic partition formula

I am trying to understand how the asymptotic partition formula $p(n) \sim \frac{e^{\pi\sqrt{\frac{2n}{3}}}}{4n\sqrt3}$ was derived for a project and have been reading and following many papers. I am ...
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### Overall idea of estimating major arcs in Waring's problem

This is copied from math.SE after a kind comment's suggestion as I am sure people here are very well knowledged in this method :) I am currently reading Vaughan's "The Hardy-Littlewood Method&...
192 views

### Birch's theorem for quartic forms in many variables

I would like to understand the application of the Hardy-Littlewood Circle Method to Birch's celebrated theorem on forms in many variables, namely the statement that the point counting function for a ...
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### Weyl sums with polynomial coefficients

Let $$f(x,N) = \sum_{0 \leq n\leq N} e(x n^2).$$ Weyl's inequality gives an estimate for $f(x,N)$ when $x$ is near a rational with small denominator. My question is: What estimates are ...
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