Given a finite group G, we study the monomial algebra R G , generated by the monomial characters of G. In particular, we note that the integral closure of R G is contained in the algebra generated by those characters χ for which their associated Artin L-function L(s, χ) is holomorphic at s 0 ∈ C \ {1}. Also, we discuss the supercharacter theoretic case.
We extend the notions of quasi-monomial groups and almost monomial groups, in the framework of supercharacter theories, and we study their connection with Artin's conjecture regarding the holomorphy of Artin L-functions.
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