Looking Backward: From Euler to Riemann

Athanase Papadopoulos ()
Additional contact information
Athanase Papadopoulos: Université de Strasbourg and CNRS, Institut de Recherche Mathématique Avancée

A chapter in From Riemann to Differential Geometry and Relativity, 2017, pp 1-94 from Springer

Abstract: Abstract We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann’s predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler.

Keywords: Bernhard Riemann; Function of a complex variable; Space; Riemannian geometry; Trigonometric series; Zeta function; Differential geometry; Elliptic integral; Elliptic function; Abelian integral; Abelian function; Hypergeometric function; Topology; Riemann surface; Leonhard Euler; Space; Integration; 01-02; 01A55; 01A67; 26A42; 30-03; 33C05; 00A30. (search for similar items in EconPapers)
Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60039-0_1

Ordering information: This item can be ordered from
http://www.springer.com/9783319600390

DOI: 10.1007/978-3-319-60039-0_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().