g2 Art. 4.— M. Kuniyeda 



liave values of tlie same type. Therefore we olitain 



r{n) = on/n). 



Thus we 11 ave 



a„ = I(n) + 0{l/7i). 



Hence, if ^(^0 < — , then 



11/ 



«« = 0(1/«); 



if I(n) > ^ , then 



a„ (^ lin}. 



46- Now wo may write 



(64) I(7i) = J-(n) + J{n), 



wliere 



ml 



V Ä7Z J '27c~s At: J 



n being a positive integer. 



If, in the neighbourhood of ^ = 0, l)oth of the functions 

 /(e*0 and /[e(2»-*^*] take the form 



where <p{x) and (p{x) are real functions of x such that 



as x^O, p and o denoting certain L-functions, then the behaviour 

 of J{n) and J(;i), as n^x, may be determined by applying the 

 results of Part I of this paper. 



