( 173 ) 
account of zi | eas + (—1)k (—) = — 1 to take each sum 
belonging to such a d, with the positive or negative sign, according 
to the number of prime divisors of d, being even or uneven. Hanes 
the values really to be subtracted being expressed by the sum 
= wd) (ase 2) 
: i 
extended to the divisors d, of n belonging to the region fm} with a 
norm surpassing unity, we then immediately arrive at the formula (1). 
For the region of the real numbers the corresponding relation 
2m Dn [7 
=" FM = Zw (d) (= f(a) 
was given as far as I know for the first time by Nasrmor in his 
treatise “Von der Summe der Zahlen, welche theilerfremd zu einer 
gegebenen Zahl MN sind und eine andere gegebene Zahl P nicht 
tiberschreiten” published in Russian in the 11% vol. of the Proceedings 
of the Math. Society in Moskow (1883). This equation of NASsIMOF, 
as well as an extension of a special case originating from K. ZsIGMONDY 
(„Zur Verallgemeinerung der Function g(m) in der Zahlentheorie,” 
Journal für die reine und angewandte Mathematik, 111rd, Vol.) 
I have considerably generalised in my treatise: “Ueber eine 
Relation des Herrn Nasrmor” contained in the 1024 vol. of the 
proceedings of the meetings of the Math. Phys. Class of the Imp. 
Academy of Sciences at Vienna. As I still wish to observe, the 
equation of Nasimor has moreover been made use of for the case 
m=o in different investigations of which I will point out as an 
example SKGuIER’s „Formes quadratiques et multiplication complexe” 
in order to avoid stating a great number of original works. 
A special case of formula (1) is the one found by DirrcuLer 
(„Recherches sur les formes quadratiques à coefficients et & indéter- 
minées complexes,” Journal fiir die reine und angewandte Mathe- 
matik, 24% vol.) 
