Og the Relatively Abelian Corpora, §3 



any composite value of ,« can ahva^ys ])e composed of those for 

 Avhicli /^"s are powers of single primes' \ The other is the confusion 

 of terminology. His proof that the division-corpus is the class- 

 corpus corresponding to the group of iiuml)ers «, such that 



« = 1 (mod. n), 



is correct only wlien the word d/vision-corpus means 



^<Hf)) 



Avhile he used the word to mean liis so-called division-corpus 

 mentioned above'\ 



Recently Fueter has given a simple example^\ which denies 

 Weber's conclusion. However, as for the relation between strahl- 

 corpora and division-corpora, there still remains a great deal of 

 obscurity. 



Let us now begin our own investigation upon this point. 



§. 17. 



Let - be an odd prime of the first degree in 1c{p), which is 

 relatively prime to o, and such tliat 



- = a + ho, h = (mod. 2), 



a and h being rational integers. Tlien as we liave seen in §. 4, 



„ _ _ ^lc"-'^x'' + Äp..2.x''---\- -^-A^x^ + B-x 



^<inuii -^.^j^p-ij.p-i_^j^^^p-6^ +o^_,^^'+l ' 



where x = snw, /> = n(-), 



a+'>-l _ 

 ;r = I.,, £ = (-1) -• ^n^-'^. 



The coefficients ^4' s and X>"s are all integers in k{(\ l), and divisible 

 by ::. Squaring l)oth sides of this formula, we obtain 



'^ " ;rV-<^-i) + (7^_,a;--'("-^> + '+C,x'+V 



i) Weber : Algebra III, §. 158. 



2) Weber: Algebra III, §. 167. In his original paper (Math. Ann., Vol. 00, p. 22), ^ve 

 find a necessary precaution against this point. 

 •è) Fueter : Math. Ann., Vol. 75. 



