256 Mr Mordell, On the representation of algebraic numbers, etc. 



Note. 



The general law of quadratic reciprocity in any field was given 

 without proof by Hilbert in the Gottinger NacJirichten for 1898, 

 page 380 in his paper "Ueber die Theorie der relativ-Abel'schen 

 Zahlkorper." In his paper "Mathematische Probleme" in the 

 Nachrichten for 1900, the investigation of the theory of the general 

 quadratic form with algebraic coefficients is proposed as problem 11. 



The law of quadratic reciprocity above was proved by Furt- 

 wangler in the third part of his paper "Die Reziprozitatsgesetze 

 fiir Potenzreste mit Primzahlexponenten in algebraischen Zahl- 

 korpern" in the Mathematische Annalen, Bd. 74, 1913. 



Manchester College of Technology. 



