830 
where 
bm @« (wv 
led Ee Je) - 
h = 1! - 
van==l ym 
Proof. Let /, and /, be two integers, prime to 4 ; if the congruence 
yma] 
1 
has no roots in z, we have 
= (0) 0, 
prva 
pm =I, 
v=l, 
since it is then impossible to find a prime number p, satisfying the 
congruence 
py =. 
Let us now, however, consider the case, that the congrence does 
possess roots and consequently has 5 incongruent roots z,, 2,,..., 25. 
The preceding identity gives 
2 Eten Aen 
pr v < Tt 
pe TZ 1 
KE 
where 
Miz 
Tr Tl) ed 
es pm < = 
put, 
v 
pm 
T=. 28°" So, 
pr” aS Ve v= 
om == l oe 
1 de 
T,= J f(r) 
= 
and 
Td 
pm <= Ve 
pe = l, 
From the preceding lemma ensues 
1 1 
Mer | = ( a 
T, = 0;——_——_} = 0 
I Va) (log «)? 
and for p™<Va 
