منابع مشابه
On Holomorphic Artin L-functions
Let K/Q be a finite Galois extension, s0 ∈ C \ {1}, Hol(s0) the semigroup of Artin L-functions holomorphic at s0. We present criteria for Artin’s holomorphy conjecture in terms of the semigroup Hol(s0). We conjecture that Artin’s L-functions are holomorphic at s0 if and only if Hol(s0) is factorial. We prove this if s0 is a zero of an L-function associated to a linear character of the Galois gr...
متن کاملOn the values of Artin L-functions
I wrote this paper in 1979, as an attempt to extend the results of Borel [2] on zeta functions at negative integers to Artin L-functions. The conceptual framework was provided by Tate’s formulation [10] of Stark’s conjectures. What I needed was a workable definition of the regulator homomorphism in complex K-theory. I discussed this with Borel at the Institute, first over lunch and then in his ...
متن کاملOn p-adic Artin L-functions II
Let p be a prime. Iwasawa’s famous conjecture relating Kubota-Leopoldt p-adic L-functions to the structure of certain Galois groups has been proven by Mazur and Wiles in [10]. Wiles later proved a far-reaching generalization involving p-adic L-functions for Hecke characters of finite order for a totally real number field in [14]. As we discussed in [5], an analogue of Iwasawa’s conjecture for p...
متن کاملPoles of Artin L - functions and the strong Artin
We show that if the L-function of an irreducible 2-dimensional complex Galois representation over Q is not automorphic then it has infinitely many poles. In particular, the Artin conjecture for a single representation implies the corresponding strong Artin conjecture. Introduction Let ρ : Gal(Q/Q) → GLn(C) be an irreducible continuous representation of the absolute Galois group of Q. Brauer [2]...
متن کاملSelberg's Conjectures and Artin L-functions
In its comprehensive form, an identity between an automorphic L-function and a "motivic" L-function is called a reciprocity law. The celebrated Artin reciprocity law is perhaps the fundamental example. The conjecture of ShimuraTaniyama that every elliptic curve over Q is "modular" is certainly the most intriguing reciprocity conjecture of our time. The "Himalayan peaks" that hold the secrets of...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1975
ISSN: 0040-8735
DOI: 10.2748/tmj/1178241036