The term “simplest ” field has been used to describe certain totally real, cyclic number fields of degrees 2, 3, 4, 5, 6, and 8. For each of these degrees, the fields are defined by a one-parameter family of polynomials with constant term ±1. The regulator of these “simplest” fields is small in an asymptotic sense: in consequence, the class number of these fields tends to be large.
Abstract.We analyze the property of period-unit integer translation (there exists a Gaussian period n and rational integer c such that n + c is a unit) in simplest quadratic, cubic, and quartic fields of arbitrary conductor. This is an extension of work of E. Lehmer, R. Schoof, and L. C. Washington for prime conductor. We also determine the Gaussian period polynomial for arbitrary conductor.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.