Gross’ conjecture for extensions ramified over four points of
Po-Yi Huang[1]
- [1] Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan
Journal de Théorie des Nombres de Bordeaux (2006)
- Volume: 18, Issue: 1, page 183-201
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topReferences
top- Noboru Aoki, Gross’ Conjecture on the Special Values of Abelian -Functions at . Commentarii Mathematici Universitatis Sancti Pauli 40 (1991), 101–124. Zbl0742.11055MR1104783
- Noboru Aoki, On Tate’s refinement for a conjecture of Gross and its generalization. J. Théor. Nombres Bordeaux 16 (2004), 457–486. Zbl1071.11064MR2144953
- David Burns, Congruences between derivatives of abelian -functions at . Preprint, 2005.
- Henri Darmon, Thaine’s method for circular units and a conjecture of Gross. Canadian J. Math. 47 (1995), 302–317. Zbl0844.11071MR1335080
- Benedict H. Gross, On the values of abelian -functions at . J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 35 (1988), 177–197. Zbl0681.12005MR931448
- David R. Hayes, The refined -adic abelian Stark conjecture in function fields. Invent. Math. 94 (1988), 505–527. Zbl0666.12009MR969242
- Po-Yi Huang, Stickelberger elements over Rational Function Fields. In preparation. Zbl1264.11095
- Joongul Lee, On Gross’ Refined Class Number Formula for Elementary Abelian Extensions. Journal of Mathematical Sciences, University of Tokyo 4 (1997), 373–383. Zbl0903.11027MR1466351
- Joongul Lee, Stickelberger elements for cyclic extensions and the order of vanishing of abelian L-functions at . Compositio Math. 138, no.2 (2003), 157–163. Zbl1057.11053MR2018824
- Joongul LeeOn the refined class number formula for global function fields. Math. Res. Lett. 11 (2004), 283–289. Zbl1112.11053MR2106227
- Michael Reid, Gross’ Conjecture for extensions ramified over three points on . Journal of Mathematical Sciences, University of Tokyo 10 no. 1 (2003), 119–138. Zbl1060.11079MR1963800
- Ki-Seng Tan, On the special values of abelian -functions. J. Math. Sci. Univ. Tokyo 1 (1994), 305–319. Zbl0820.11069MR1317462
- M. Yamagishi, On a conjecture of Gross on special values of -functions. Math. Z. 201 (1989), 391–400. Zbl0689.12002MR999736