154 



R. FUJIKAWA. 



respectively. Tlie iiinneratov 7' + V s- imist be .so (leteriniiied tli;it it 

 VMtiishes ill q jK)int^! '\i mikI. besides, in niiother set oi' q ])(>iiits 



e'v ICr I -6v\, > = 1,'^, a, q. 



It will 1)6 convenient to write ^v+p instend of s;, iind then /' + ^^s 

 vanishes in 2q ])oints 



On |.2V 1 -vK /^ = 1, '^, 3, ... (7, q+\, ... 'i^. 

 Equation (1.) then takes the form 



Ai =2'/ .7^ 



(2.) 2 ^ = 0. 



We now take for the fundamental irnitionalitv Iviemann's form 



and write 



f7? 



so that 





Sil // . 



Two cases are to be distin<iuished accordini»' as n is odd or e^■en. 



AVhen // is odd, put n = 2in+ 1=^:2']—], and lei one of the 'Jq jioints 

 in which J'+(Js vani.shes, coincide with the point { >!' | o } :>nd the 

 l'ciiiaininu' (2]— 1) points with the p(jint | ,2- | ,s}. E(piation (2.) then 

 becomes 



