Stark's conjecture in multi-quadratic extensions, revisited

David S. Dummit; Jonathan W. Sands; Brett Tangedal

Journal de théorie des nombres de Bordeaux (2003)

  • Volume: 15, Issue: 1, page 83-97
  • ISSN: 1246-7405

Abstract

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Stark’s conjectures connect special units in number fields with special values of L -functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent 2 . For biquadratic extensions and most others, we prove more, establishing the conjecture in full.

How to cite

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Dummit, David S., Sands, Jonathan W., and Tangedal, Brett. "Stark's conjecture in multi-quadratic extensions, revisited." Journal de théorie des nombres de Bordeaux 15.1 (2003): 83-97. <http://eudml.org/doc/249103>.

@article{Dummit2003,
abstract = {Stark’s conjectures connect special units in number fields with special values of $L$-functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent $2$. For biquadratic extensions and most others, we prove more, establishing the conjecture in full.},
author = {Dummit, David S., Sands, Jonathan W., Tangedal, Brett},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Stark's conjecture; Artin -functions; Abelian extensions; units; class field theory},
language = {eng},
number = {1},
pages = {83-97},
publisher = {Université Bordeaux I},
title = {Stark's conjecture in multi-quadratic extensions, revisited},
url = {http://eudml.org/doc/249103},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Dummit, David S.
AU - Sands, Jonathan W.
AU - Tangedal, Brett
TI - Stark's conjecture in multi-quadratic extensions, revisited
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 1
SP - 83
EP - 97
AB - Stark’s conjectures connect special units in number fields with special values of $L$-functions attached to these fields. We consider the fundamental equality of Stark’s refined conjecture for the case of an abelian Galois group, and prove it when this group has exponent $2$. For biquadratic extensions and most others, we prove more, establishing the conjecture in full.
LA - eng
KW - Stark's conjecture; Artin -functions; Abelian extensions; units; class field theory
UR - http://eudml.org/doc/249103
ER -

References

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  1. [1] G. Janusz, Algebraic number fields. Academic Press, New York, 1973. Zbl0307.12001MR366864
  2. [2] J.W. Sands, Galois groups of exponent two and the Brumer-Stark conjecture. J. Reine Angew. Math.349 (1984), 129-135. Zbl0521.12009MR743968
  3. [3] J.W. Sands, Two cases of Stark's conjecture. Math. Ann.272 (1985), 349-359. Zbl0554.12006MR799666
  4. [4] H.M. Stark, L-functions at s = 1 IV. First derivatives at s = 0. Advances in Math.35 (1980), 197-235. Zbl0475.12018MR563924
  5. [5] J.T. Tate, Les conjectures de Stark sur les fonctions L d'Artin en s = 0. Birkhäuser, Boston, 1984. Zbl0545.12009

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