Skip to main content

Abel’s Motivations

  • 2050 Accesses

Part of the Lecture Notes in Mathematics book series (HISTORYMS,volume 2162)

Abstract

Abel’s works, which we mentioned in the last two chapters, are the first in which the modern notion of genus appeared. Nevertheless, it was in a hidden form, a little like a secondary character remaining in the shadows, devoid of name. It is worth trying to understand better the general problems which preoccupied Abel at that time, of which [128] is only an expression. Happily for us, Abel wrote about these problems in an 1828 letter [2] to Legendre

Keywords

  • Hidden Form
  • Modern Notion
  • Arbitrary Algebraic Function
  • Abelian Integrals
  • Arbitrary Relation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. N.H. Abel, Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes, Presented at the French Académie des Sciences in Paris on the 30 October 1826. Republished in Œuvres complètes de Niels Henrik Abel, vol. I, ed. by L. Sylow, S. Lie (Grondahl and Son, Christiania, 1881), pp. 145–211

    Google Scholar 

  2. N.H. Abel, Lettre à Legendre du 25 Novembre 1828. Republished in Œuvres complètes de Niels Henrik Abel, vol. II, ed. by L. Sylow, S. Lie (Grondahl and Son, Christiania, 1881), pp. 271–279

    Google Scholar 

  3. S.L. Kleiman, What is Abel’s theorem anyway? in [127], pp. 395–440

    Google Scholar 

  4. A.-M. Legendre, Traité des fonctions elliptiques, Tome Premier (Huzard-Courcier, Paris, 1825)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Popescu-Pampu, P. (2016). Abel’s Motivations. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_11

Download citation