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Po-Yi Huang
Gross’ conjecture for extensions ramified over four points of $\mathbb{P}^1$
Journal de théorie des nombres de Bordeaux, 18 no. 1 (2006), p. 183-201, doi: 10.5802/jtnb.539
Article PDF | Reviews MR 2245881 | Zbl 05070453

Résumé - Abstract

In this paper, under a mild hypothesis, we prove a conjecture of Gross for the Stickelberger element of the maximal abelian extension over the rational function field unramified outside a set of four degree-one places.

Bibliography

[1] Noboru Aoki, Gross’ Conjecture on the Special Values of Abelian $L$-Functions at $s=0$. Commentarii Mathematici Universitatis Sancti Pauli 40 (1991), 101–124.  MR 1104783 |  Zbl 0742.11055
[2] Noboru Aoki, On Tate’s refinement for a conjecture of Gross and its generalization. J. Théor. Nombres Bordeaux 16 (2004), 457–486. Cedram |  MR 2144953 |  Zbl 1071.11064
[3] David Burns, Congruences between derivatives of abelian $L$-functions at $s=0$. Preprint, 2005.
[4] Henri Darmon, Thaine’s method for circular units and a conjecture of Gross. Canadian J. Math. 47 (1995), 302–317.  MR 1335080 |  Zbl 0844.11071
[5] Benedict H. Gross, On the values of abelian $L$-functions at $s=0$. J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 35 (1988), 177–197.  MR 931448 |  Zbl 0681.12005
[6] David R. Hayes, The refined $p$-adic abelian Stark conjecture in function fields. Invent. Math. 94 (1988), 505–527.  MR 969242 |  Zbl 0666.12009
[7] Po-Yi Huang, Stickelberger elements over Rational Function Fields. In preparation.
[8] Joongul Lee, On Gross’ Refined Class Number Formula for Elementary Abelian Extensions. Journal of Mathematical Sciences, University of Tokyo 4 (1997), 373–383.  MR 1466351 |  Zbl 0903.11027
[9] Joongul Lee, Stickelberger elements for cyclic extensions and the order of vanishing of abelian L-functions at $s=0$. Compositio Math. 138, no.2 (2003), 157–163.  MR 2018824 |  Zbl 1057.11053
[10] Joongul Lee On the refined class number formula for global function fields. Math. Res. Lett. 11 (2004), 283–289.  MR 2106227 |  Zbl 02152361
[11] Michael Reid, Gross’ Conjecture for extensions ramified over three points on $\mathbb{P}^1$. Journal of Mathematical Sciences, University of Tokyo 10 no. 1 (2003), 119–138.  MR 1963800 |  Zbl 1060.11079
[12] Ki-Seng Tan, On the special values of abelian $L$-functions. J. Math. Sci. Univ. Tokyo 1 (1994), 305–319.  MR 1317462 |  Zbl 0820.11069
[13] M. Yamagishi, On a conjecture of Gross on special values of $L$-functions. Math. Z. 201 (1989), 391–400.  MR 999736 |  Zbl 0689.12002