A relationship between the nonexistence of generalized bent functions and class groups

Abstract

A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations. At the same time, a method is given which can be used to simplify the known results. Then we give the bounds and the meaning in algebraic number theory of the parameters in our results.