Karl Weierstraß and the theory of Abelian and elliptic functions

  • Peter Ullrich


The starting point for Weierstraß’s mathematical research and his career was the theory of elliptic and, more general, Abelian functions: His final decision to devote his life to mathematics resulted from his success in finding an alternative proof of one of Abel’s results on elliptic functions. And Weierstraß received his recognition in academic community because of his complete solution of the prestigious Jacobi inversion problem for hyperelliptic Abelian functions in his 1854 paper.

Weierstraß’s contributions to the fundaments of analysis, in particular to the theory of analytic functions of one and several complex variables, mainly originated in the foundational problems that he saw himself confronted with when attacking problems concerning the type of functions mentioned above. This was in particular the case after Riemann had given his view of the theory of general Abelian functions in 1857 which represented an other way of approach to the problem than Weierstraß’s but had some deficits in the details of the argumentation.


Elliptic Function Power Series Expansion Elliptic Integral Theta Series Elliptic Case 
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Copyright information

© Springer Fachmedien Wiesbaden 2016

Authors and Affiliations

  • Peter Ullrich
    • 1
  1. 1.Mathematisches InstitutUniversität Koblenz-LandauKoblenzGermany

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