827 
h is the number of positive integers <, prime to k, b is the 
number of incongruent roots z of the congruence 
ea = 
and the sum 
S Fw 
tT 1 
uam=l ym 
is extended over all the positive integers u, for which the congruence 
nam | 
has roots in z. 
$ 2. Lemma. 
Va f 5) 
Ss Fey log? oy, 
i/ 
0 
mi 
ym 
1 
x am 
Se EN ES —— 
alll A ) 3 = 7 
ai 
ms Sf) +O : ‘ 
t= t v1 1 log v 
and IE 
yin a 
Proof. From the relations satisfied by the functions /’ and /, 
it follows, u being an integer, for which v, has the value », that 
n= f(t ee 0 (v,.") = Our) 
ot 1 
and for — >s >-——— + u the left member of the identity 
m m1 
1 : ipl See 
i Tate 2 plm 2)is—#) EERE p= VS 
dr Mi 
is a convergent product and consequently the right member a con- 
vergent sum, therefore 
Hy "(a5 x Ov” 
Be tie Een 
Jil vs v=2 v 
ey > m 
bed 
On neer Oli 
y=2 VST 
ey > m 
Hence 
