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ON ARTIN LFUNCTIONS
"... Artin spent the first 15 years of his career in Hamburg. Weil characterized this period of Artin’s career as a “love affair with the zeta function ” [72]. Chevalley, in his obituary of Artin [12], pointed out that Artin’s use of zeta functions was to discover exact algebraic facts as opposed to esti ..."
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to estimates or approximate evaluations. In particular, it seems clear to me that during this period Artin was quite interested in using the Artin Lfunctions as a tool for finding a nonabelian class field theory, expressed as the desire extend results from relative abelian extensions to general extensions
On the values of Artin Lfunctions
 WALTER D. NEUMANN AND JUN YANG
, 1980
"... 0. Information I wrote this paper in 1979, as an attempt to extend the results of Borel [2] on zeta functions at negative integers to Artin Lfunctions. The conceptual framework was provided by Tate’s formulation [10] of Stark’s conjectures. What I needed was a workable definition of the regulator h ..."
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0. Information I wrote this paper in 1979, as an attempt to extend the results of Borel [2] on zeta functions at negative integers to Artin Lfunctions. The conceptual framework was provided by Tate’s formulation [10] of Stark’s conjectures. What I needed was a workable definition of the regulator
Extreme values of Artin Lfunctions and class numbers
 Compositio Math
"... Assuming the GRH and Artin conjecture for Artin Lfunctions, 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 ..."
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Cited by 8 (1 self)
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Assuming the GRH and Artin conjecture for Artin Lfunctions, 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
Irreducible representations and Artin Lfunctions of quasicyclotomic fields
, 2008
"... We determine all irreducible representations of primary quasicyclotomic fields in this paper. The methods can be applied to determine the irreducible representations of any quasicyclotomic field. We also compute the Artin Lfunctions for a class of quasicyclotomic fields. 1 ..."
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We determine all irreducible representations of primary quasicyclotomic fields in this paper. The methods can be applied to determine the irreducible representations of any quasicyclotomic field. We also compute the Artin Lfunctions for a class of quasicyclotomic fields. 1
Selberg’s conjectures and Artin Lfunctions
 1–14. zeros of RankinSelberg Lfunctions 31
, 1994
"... In its comprehensive form, an identity between an automorphic Lfunction and a “motivic ” Lfunction 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 th ..."
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Cited by 8 (1 self)
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In its comprehensive form, an identity between an automorphic Lfunction and a “motivic ” Lfunction 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
Total Degree Bounds for Artin Lfunctions and Partial Zeta Functions
, 2003
"... this paper, schemes, morphisms and sheaves de ned over the base eld F q are denoted by letters with subscripts 0. We indicate the base extension from F q to F by dropping the subscripts 0. Schemes and morphisms are separated and of nite type ..."
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Cited by 3 (3 self)
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this paper, schemes, morphisms and sheaves de ned over the base eld F q are denoted by letters with subscripts 0. We indicate the base extension from F q to F by dropping the subscripts 0. Schemes and morphisms are separated and of nite type
Diagonal cycles and Euler systems II: The Birch and SwinnertonDyer conjecture for HasseWeilArtin Lfunctions
"... This article establishes new cases of the Birch and SwinnertonDyer conjecture in analytic rank 0, for elliptic curves over Q viewed over the elds cut out by certain selfdual Artin representations of dimension at most 4. When the associated Lfunction vanishes (to even order 2) at its central p ..."
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Cited by 5 (5 self)
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This article establishes new cases of the Birch and SwinnertonDyer conjecture in analytic rank 0, for elliptic curves over Q viewed over the elds cut out by certain selfdual Artin representations of dimension at most 4. When the associated Lfunction vanishes (to even order 2) at its central
TADIC LFUNCTION OF WITT EXTENSIONS
, 2009
"... The Tadic Lfunction of the torus given by a Witt extension is studied. Generic Newton polygon of the Tadic Lfunction as well as that of the Artin Lfunction are determined. ..."
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The Tadic Lfunction of the torus given by a Witt extension is studied. Generic Newton polygon of the Tadic Lfunction as well as that of the Artin Lfunction are determined.
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