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

In: From Riemann to Differential Geometry and Relativity

Author

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  • Christian Houzel

    (Universit Paris Diderot, Laboratoire SPHERE, UMR 7219)

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.

Suggested Citation

  • Christian Houzel, 2017. "Riemann’s Memoir Über das Verschwinden der $$\vartheta $$ -Functionen," Springer Books, in: Lizhen Ji & Athanase Papadopoulos & Sumio Yamada (ed.), From Riemann to Differential Geometry and Relativity, pages 125-134, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60039-0_4
    DOI: 10.1007/978-3-319-60039-0_4
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