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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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
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
S.L. Kleiman, What is Abel’s theorem anyway? in [127], pp. 395–440
A.-M. Legendre, Traité des fonctions elliptiques, Tome Premier (Huzard-Courcier, Paris, 1825)
Author information
Authors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-3-319-42312-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42311-1
Online ISBN: 978-3-319-42312-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)
