Riemann’s Memoir Über das Verschwinden der $$\vartheta $$ -Functionen

Christian Houzel ()
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Christian Houzel: Universit Paris Diderot, Laboratoire SPHERE, UMR 7219

A chapter in From Riemann to Differential Geometry and Relativity, 2017, pp 125-134 from Springer

Abstract: Abstract In the second part of his great memoir Theorie der Abel’schen Functionen (1857), Riemann gives a solution to Jacobi’s problem of inversion for the general case of integrals of algebraic functionsIntegral Abelian Abelian integral , now called Abelian integrals. The case of hyperelliptic integralsIntegral hyperelliptic Hyperelliptic integral had been treated, for the genus 2, by Göpel and Rosenhain and, for any genus, by Weierstrass in a series of memoirs between 1848 and 1856. The proof developed by Riemann in his 1857 paper is not complete and the memoir Über das Verschwinden der $$\vartheta $$ -Functionen (1865) completes it.

Keywords: Rosenhain; Schen Functionen; Abelian Integrals; Weierstrass; Algebraic Functions (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-60039-0_4

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