K Ramachandra - Srinivasa Ramanujan (The inventor of the circle method) (22-12-1887 to 26-4-1920)

hrj:102 - Hardy-Ramanujan Journal, January 1, 1987, Volume 10 - 1987 - https://doi.org/10.46298/hrj.1987.102
Srinivasa Ramanujan (The inventor of the circle method) (22-12-1887 to 26-4-1920)

Authors: K Ramachandra

Ramanujan's first letter to Hardy states an asymptotic formula for the coefficient of $x^n$ in the expansion of $(\sum_{m=-\infty}^{\infty}(-1)^mx^{m^2})^{-1}$ which can be regarded as the genesis of the circle method. In this paper, we try to give some indication of the possible intuition of Ramanujan in his discovery of the circle method. We discuss briefly the Goldbach, Waring and partition problems. At the end of the paper, there is a brief discussion on Ramanujan's $\tau$ function


Volume: Volume 10 - 1987
Published on: January 1, 1987
Imported on: March 3, 2015
Keywords: Waring's problem,partition function,Goldbach conjecture,circle method,[MATH] Mathematics [math]


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