On the Eelatively Abelian Corpora. 43 



Next, since 



dj: can be transformed as follows : 



f7, = 4(y,_i-lxT/. + l)- 

 Now, from the relation 



we conclude that l)oth y,-{> and ji,-o are divisible by />-l. Con- 

 sequently both 



r>.- + 1 ^ VirzJ^ ^ Ilk' - .'^' 



/y— 1 // — i /' — I 



, and zi+L = i^+j/;-."- 



must be algebraic integers. But, since 



it folloAvs that 



Tlie corpus K{Y,) can be defined l)y an integer 



But, the relative discriminant of this integer with respect to 



B, 



^=16,rtxa:^.i-16, 



since it can easily be inferred from (22) that z,., is an algel^raic 

 unity. Hence Ave see that the relative discriminant of K(Y,) with 

 respect to Ä%_i) can contain no ideal factor relatively prime to 2. 

 The corpus Ki^y,) can l)e defined l)y an integer 





whose relative discriminant with respect to K{Y,) is 



(Z'-l)"^' 



