Major Progress on a Problem of Ramanujan

  • Krishnaswami Alladi


The theorem of Lagrange that every positive integer is a sum of at most four squares is one of the most appealing in all of mathematics. Ramanujan considered extensions of this theorem by listing a set of universal quadratic forms, namely those which represent all positive integers. This article is a report of the work of Manjul Bhargava and Jonathan Hanke, who solved a conjecture of Conway of determining the universality of quadratic forms, a problem that has its origins in Ramanujan’s work.

Copyright information

© Springer India 2013

Authors and Affiliations

  • Krishnaswami Alladi
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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