Stark's conjecture in multi-quadratic extensions, revisited
Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 83-97.

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.

Les conjectures de Stark relient les unités spéciales dans les corps de nombres à certaines valeurs des fonctions L attachées à ces corps. Nous considérons le cas d’une extension abélienne, et nous établissons la relation fondamentale de la conjecture de Stark lorsque son groupe de Galois est d’exposant 2. Nous montrons que la conjecture est entièrement vérifiée pour les extensions biquadratiques ainsi que dans de nombreux autres cas.

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     author = {David S. Dummit and Jonathan W. Sands and Brett Tangedal},
     title = {Stark's conjecture in multi-quadratic extensions, revisited},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {83--97},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     doi = {10.5802/jtnb.388},
     zbl = {1047.11108},
     mrnumber = {2019002},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.388/}
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David S. Dummit; Jonathan W. Sands; Brett Tangedal. Stark's conjecture in multi-quadratic extensions, revisited. Journal de Théorie des Nombres de Bordeaux, Volume 15 (2003) no. 1, pp. 83-97. doi : 10.5802/jtnb.388. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.388/

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[4] H.M. Stark, L-functions at s = 1 IV. First derivatives at s = 0. Advances in Math. 35 (1980), 197-235. | MR | Zbl

[5] J.T. Tate, Les conjectures de Stark sur les fonctions L d'Artin en s = 0. Birkhäuser, Boston, 1984. | Zbl

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