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Bernhard Riemann Remarks on his Life and Work

Abstract

The first part contains a few facts about Riemann taken from correspondence (of Riemann and of Dedekind), and then describes Riemann’s letter to Weierstrass concerning his paper on the distribution of primes. It is followed by a brief outline of the paper itself.

The second part deals with his course of Wintersemester 1858/59 on the hypergeometric series, which anticipated by a decade important work of L. Fuchs and H.A. Schwarz. The course also contains Riemann’s ideas on what we would now call finite dimensional local systems on P 1 \ S where S is finite.

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References

  1. Bernhard Riemann, Gesammelte mathematische Werke und wissenschaftlicher Nachlass und Nachträge. Collected papers. New edition 1990, edited by Raghavan Narasimhan, with contributions by several people.- 1st edition 1876, 2nd edition 1892, edited by Heinrich Weber and Richard Dedekind. Nachträge 1st edition 1902, edited by Max Noether and Wilhelm Wirtinger. Springer Verlag / BSB B.G. Teubner Verlagsgesellschaft.

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Correspondence to Raghavan Narasimhan.

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This text is based on a talk at the RISM conference in Verbania, Intra, Italy, April 19–24, 2009.

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Narasimhan, R. Bernhard Riemann Remarks on his Life and Work. Milan J. Math. 78, 3–10 (2010). https://doi.org/10.1007/s00032-010-0116-5

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Mathematics Subject Classification (2010)

  • 01A70
  • 01A55
  • 11N05
  • 11S40
  • 34M03
  • 34M35

Keywords

  • Riemann’s life
  • zeta function
  • distribution of primes
  • monodromy