Expositio paper exp-20261009-379e5b
The Circle Method, the j-Function, and Partitions
The circle method was first used by Hardy and Ramanujan in 1918 to investigate the asymptotic growth of the partition function, which counts the number of ways to write n as a sum of positive integers. This expository paper shows two examples of how Radema…
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Abstract
The circle method was first used by Hardy and Ramanujan in 1918 to investigate the asymptotic growth of the partition function, which counts the number of ways to write n as a sum of positive integers. This expository paper shows two examples of how Rademacher used a variant of the circle method to produce series representations for the partition function and for the coefficients of the j function.
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