( VI ) 



The function Mi,ji (.y) is regular in that part of the phxne lying on 

 the right side of the continuous curve (incl. the curve itself) 



1 — for t > 3, 



log"- 1 = 



'ö=l— for — 3<<<3, 



%« 3 = = 



a=i for « < — 3 



loga{-t) = 



and for « > 3, 1 — ; < a < 2 it is 



= log^ t = = 



\iMb,h{(J-{-ti)\ = \Mb,h{o-ti)\<:iog^t (13) 



§ 4. In § 2 of my paper ^) "On the function n{k) occurring in 

 the theory of numbers" ("Ueber die zahlentheoretische Funktion (lik)") 

 the relation 



k=l 2—x^i k=l 



is developed, where the integral is taken along the straight line. In 

 like manner v^e find here, vt^hen the sign 2£' means that k has but 

 to assume all those numbers of the interval of summation v^hich are 

 = h (mod. b), 



k=l -2—xH k=\ 



-. r -Jh,h{s)ds^O{l). . . (14) 



2jr^ 



9 — r2; 



— Mb,h («) ^ 



taken along the closed path ABCDEFA, where A — 2—.r\B=2 -f w\ 



1 1 1 , 



C—1 h wH, D—l h 3i, E—l — - — - - 3i, and 



log<^{x') ^ log^^ ^ log"3 



F=l xH, where the segments AB, BC, DE, FA are 



log'^{x'') 



rectilinear, CD denotes the arc of the curve 



8=1 yti (^-^ > i > 3) 



logH ^ = := ' 



1) Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften in Wien, math.- 

 naturw. Klasse, Bd. 112, Abt. 2a, 1903, S. 537-570. 



