Research in Paderborn: Note on Hurwitz’ Equation
نویسنده
چکیده
Introduction The differential equation H(y) = 0 (see below) due to Hurwitz goes back to the famous work “Ueber die Transformation siebenter Ordnung der elliptischen Functionen” of F. Klein [14]. In this work, Klein made an important contribution to the much discussed question of the solvability of algebraic equations by means of elliptic modular functions. In order to investigate the transformation of seventh order of elliptic functions (see also [12], [13]), starting from the simple group G168 consisting of 168 linear substitutions, Klein constructed the Riemann surface [14, p. 441] F ( ; ; ) = 3 + 3 + 3 = 0: (9)
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