155 
Then P can be expressed as a linear homogeneous function of xi. 
Proof: 
m, ®, +M,0, 
*o(nu|o,; ©,)—f(@,, o,) Lo(u— = @1, @5)- 
1] 7] 
——— Ra (Os Wh) Ue cecppaesoaleys cpsiele siaeceys\s) elare eas (3) 
e 
m,,m,—0...1—1 
 ( | Ree e(™ aL 02 ) (nu— Ao, + po, Ne (nu — hoy + po, | 0, 02) 
aD if n 2n n 
hn’ nm [From (2) 
“6 (nu | @, 0) 
Lael aoa 
iy an 
9 (Amy yng ) (nu — 20; + mo) QM». (n—1) (u— 20, + Hey) 
n 2n 2 7" 
n—1 
~ if (@), @g) II o( Aw, + Lo 6) ) Ma Da) 
1 Daisey ae U — AW, + HO, — MO; + Mp0, why eins 
lg Cece 2 
ae 0 n n 
from equations (2) and (3). 
Whenceco (nu | @,, @,) 
2 «  isac-product of n? factors. 
n’n 
Whose residue sum, 
: n—1 n—1 
S= 401 + wo, +n ii @, +n (ee) Ws 3 
moreover there are n? different quantities 
io (mu) | or, o))- 
Nye 
2 
n on 
If now, m define n? quantities 
n?—1 
wia= OF.) ML er GUS UiNl)oo tooo ooebabocen bees oMOcncpODU DO ob dina GEBincr toc (4) 
= 
n,—1 
Such that > a; j = (i=0....n?—1) 
i=0 
*Jordan: ‘‘Coursd’Analyse,’’ Tome 2, p. 388. 
+ Klein: ‘“ Vorlesungen iiber die Theorie der Elliptischen Modulfunctionen,’’ Vol. 
DS pe26: 
