On a theorem of higher reciprocity
Albert Leon Whiteman · Bulletin of the American Mathematical Society · 1937
WHITEMANf1. Introduction, Let 35 denote the totality of polynomials in an indeterminate x, with coefficients in a fixed Galois field GF(p*) of order p r .Let P be a primary irreducible polynomial in 35; then, if A is any polynomial in 3) not divisible by P, we define {^4|P} as that element in GF(p T ) for which &}-where v is the degree of P.We have then the following theorem of reciprocity due to H. KuhneJ and rediscovered by Schmidt § and Carlitz.||If P and Q are primary irreducible polynomials in 35 of degree v and p respectively y then £}-<-«-£}• If M=Pi n • • • P k ak and (-4, M) = 1 we use the definition,