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The Möbius–Wall congruences for p-adic L-functions of CM elliptic curves


In this paper we prove, under a technical assumption, the so-called “Möbius–Wall” congruences between abelian p-adic L-functions of CM elliptic curves. These congruences are the analogue of those shown by Ritter and Weiss for the Tate motive, and offer strong evidences in favor of the existence of non-abelian p-adic L-functions for CM elliptic curves.

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[2]Bouganis, Th.. Non abelian p-adic L-functions and Eisenstein series of unitary groups; the CM-method, preprint. arXiv:1107.1377v2[math.NT].
[3]Coates, J., Fukaya, T., Kato, K., Sujatha, R. and Venjakob, O.. The GL 2-main conjecture for elliptic curves without complex multiplication. Publ. Math. Inst. Hautes. Études Sci. 101 (2005), no. 1, 163208.
[4]Fukaya, T. and Kato, K.. A formulation of conjectures on p-adic zeta functions in non-commutative Iwasawa theory. Proceedings of the St. Petersburg Mathematical Society, vol XII (Providence RI). Amer. Math. Soc. Transl. Ser. 2 vol 219 (2006).
[5]Hara, T.. Iwasawa theory of totally real fields for certain non-commutative p-extensions. J. Number Theory 130 (4), (2010), 10681097.
[6]Harris, M., Li, J.-S. and Skinner, C.. p-adic L-functions for unitary Shimura varieties, I: Construction of the Eisenstein measure. Documenta Math. Extra Volume: John H. Coates' Sixtieth Birthday (2006), 393–464.
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[8]Kakde, M.. Proof of the main conjecture of non-commutative Iwasawa theory of totally real number fields. Invent. Math. DOI 10.1007/s00222-012-0436-x, (2012).
[9]Kato, K.. Iwasawa theory of totally real fields for Galois extensions of Heisenberg type, preprint.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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