Values of twisted Artin L-functions
نویسندگان
چکیده
منابع مشابه
On 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 کاملExtreme values of Artin L-functions and class numbers
Assuming the GRH and Artin conjecture for Artin L-functions, we prove that there exists a totally real number field of any fixed degree (> 1) with an arbitrarily large discriminant whose normal closure has the full symmetric group as Galois group and whose class number is essentially as large as possible. One ingredient is an unconditional construction of totally real fields with small regulato...
متن کاملOn 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 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 کاملArtin L-functions of small conductor
We study the problem of finding the Artin L-functions with the smallest conductor for a given Galois type. We adapt standard analytic techniques to our novel situation of fixed Galois type and obtain much improved lower bounds on the smallest conductor. For small Galois types we use complete tables of number fields to determine the actual smallest conductor.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2014
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-014-0692-7