Biography hardy-ramanujan-littlewood circle method
Circle method product management
Biography hardy-ramanujan-littlewood circle method...
Hardy–Ramanujan–Littlewood circle method
Technique in analytic number theory
In mathematics, the Hardy–Ramanujan–Littlewood circle method is a technique of analytic number theory.
It is named for G. H. Hardy, S. Ramanujan, and J. E. Littlewood, who developed it in a series of papers on Waring's problem.
History
The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.
How did ramanujan learn math
It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines. Hundreds of papers followed, and as of 2022[update] the method still yields results.
The method is the subject of a monograph Vaughan (1997) by R. C. Vaughan.
Outline
The goal is to prove asymptotic behavior of a series: to show that an ~ F(n) for some