On Artin’s L-functions. Iii: One Dimensional Characters by Florin Nicolae at Berlin and Bucharest
نویسنده
چکیده
Let K/Q be a finite Galois extension with the Galois group G, and let χ be a nontrivial irreducible character ofG. Artin’s conjecture predicts that the L-function L(s, χ,K/Q) is holomorphic in the whole complex plane ([1], P. 105). Let χ1, . . . , χr be the irreducible nontrivial characters of G. The corresponding L-functions L(s, χ1), . . . , L(s, χr) are algebraically independent over C ([2], Corollary 4, P. 183). Let A := C[L(s, χ1), . . . , L(s, χr)] be the C-Algebra generated by the meromorphic functions L(s, χ1), . . . , L(s, χr). It is isomorphic to the algebra of polynomials in r variables over C. Let O(C) be the C-algebra of holomorphic functions in C. Artin’s conjecture is:
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