10 



Art. 5.- T. Takonondii : 



Hence, when « is any prime in h{(>), the coefficients of P,.(.t), ex- 

 cept the constant term, are all divisible hy /^-. 



The same property holds also for /iSV; whence follows, by 

 Eisenstein's theorem, that ^^,. is irredücil)le in /{/'). 



§. 4. 



The only thing we have hitherto assumed concerning the 

 function ^^(^/) is the relation 



which gives 



r/, = 0. 



Here, as well as hereafter, we shall completely specialise the 

 function b}' the additional conditions : 



C: = 



f.,= ^^ 



1' 



,-1 



,^1 0) + 0)' 



-1' 



(3) 



and consequently 



(J., = àe^c^f. = 





Then, let us put 



.(„) = «") 



V r/.i 



-^4 



The ambiguit}' in the former definition of t(i/) is thus removed. 



Now, let 0, A, 7>, C'be the vertices of the parallelogram in 

 the Gaussian plane, corresponding respectively to the values 



qi := 0, (O, oj-\-(o\ CO ; 



and let OE, OF be ch'awn perpendicular to AB. BC respectively, 

 and P(r, Pi/ perpendicular te CO, 0^4 respectively. Since 



1) Takcnouchi.: loc. cit. 



