The nonvanishing of certain character sums
Author: S. Ullom
Journal: Proc. Amer. Math. Soc. 45 (1974), 164-166
MSC: Primary 12A55; Secondary 10G05, 12A35
MathSciNet review: 0354611
Abstract: Let be a Dirichlet character with conductor and , summation over integers prime to and . It is well known that the nonvanishing of the Dirichlet -function at implies for imaginary, i.e. . This article provides a purely algebraic proof that when the conductor is a prime power and the imaginary is either a faithful character or has order a power of 2.
Keywords: Character sum, cyclotomic field, class number, integral group ring
Article copyright: © Copyright 1974 American Mathematical Society