# 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&...
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### 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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### Goldbach's problem in algebraic number fields [duplicate]

Are there any results on the representation of numbers in algebraic number fields as the sum of primes in the ring of integers in that field? There are some results for Waring's problem in other ...
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