On Artin <i>L</i>-functions
نویسندگان
چکیده
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...
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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 ...
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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...
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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 کاملGrowth functions for Artin monoids
In [S1] we showed that the growth function PM (t) for an Artin monoid of finite type M is a rational function of the form 1/NM (t) where NM (t) is a polynomial1, and gave three conjectures on the denominator polynomial NM (t). In the present note, we remove this assumption on M by showing the result for any type M . Then we give renewed three conjectures on the denominator poynomial NM (t) for ...
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ژورنال
عنوان ژورنال: Japanese journal of mathematics. New series
سال: 1977
ISSN: 0289-2316,1861-3624
DOI: 10.4099/math1924.3.369