Refined class number formulas for 𝔾 m
Barry Mazur1; Karl Rubin2
1 Department of Mathematics Harvard University Cambridge, MA 02138, USA
2 Department of Mathematics UC Irvine Irvine, CA 92697, USA
Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 1, pp. 185-211.

We formulate a generalization of a “refined class number formula” of Darmon. Our conjecture deals with Stickelberger-type elements formed from generalized Stark units, and has two parts: the “order of vanishing” and the “leading term”. Using the theory of Kolyvagin systems we prove a large part of this conjecture when the order of vanishing of the corresponding complex L-function is 1.

Nous formulons une généralisation d’une “formule du nombre de classes raffinée” de Darmon. Notre conjecture concerne des éléments de type Stickelberger formés à partir d’unités de Stark généralisées. En utilisant la théorie des systèmes de Kolyvagin, nous démontrons une grande partie de cette conjecture lorsque l’ordre d’annulation de la fonction L complexe correspondante est 1.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.934
Classification: 11R42,  11R27,  11R23,  11R29
Keywords: Class number formulas, Euler systems, Kolyvagin systems, Stark conjectures, L-functions.
Barry Mazur 1; Karl Rubin 2

1 Department of Mathematics Harvard University Cambridge, MA 02138, USA
2 Department of Mathematics UC Irvine Irvine, CA 92697, USA 
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Barry Mazur; Karl Rubin. Refined class number formulas for $\mathbb{G}_m$. Journal de Théorie des Nombres de Bordeaux, Volume 28 (2016) no. 1, pp. 185-211. doi : 10.5802/jtnb.934. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.934/

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