How Rademacher Derived His Formula for Partitioning Integers

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SUMMARY

Rademacher's formula for partitioning integers is derived using Farey sequences and Ford circles, as indicated in the discussion. The number 24 is significant in this context, appearing in the coefficients of the partition function. The formula involves complex sums of exponentials to the base e, which are essential for understanding the partitioning process. John Conway's layman's book on number theory references this formula but lacks a detailed derivation.

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  • Understanding of Farey sequences
  • Familiarity with Ford circles
  • Knowledge of partition functions in number theory
  • Basic concepts of exponential functions
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Can anyone sketch out how Rademacher wound up with his formula for the number of ways to partition an integer? Or at least explain why the number 24 shows up in it?

(In the graphic link below, the A coefficients are themselves defined as a certain rather complicated sum of exponentials to the base e.)
 

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Yes, Nate. In fact I grabbed the formula image file from that very page that you linked. I first came upon the formula in a layman's book on number theory by John Conway, but that book didn't offer a derivation if I recall.
 
Reminds of the solution to the third degree equation!
 
Bumping this up in case some of the newer members can provide some insight.
 

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