Circle Method

The circle method is a method employed by Hardy, Ramanujan, and Littlewood to solve many asymptotic problems in additive number theory, particularly in deriving an asymptotic formula for the partition function P. The circle method proceeds by choosing a circular contour satisfying certain technical properties (Apostol 1997). The method was modified by Rademacher using a different contour in his derivation of the convergent asymptotic formula for the partition function P.

REFERENCES:

Apostol, T. M. "The Plan of the Proof." §5.2 in Modular Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 95-96, 1997.