{
  "id": "1411.1184",
  "version": "v1",
  "published": "2014-11-05T08:22:53.000Z",
  "updated": "2014-11-05T08:22:53.000Z",
  "title": "On the transfer congruence between $p$-adic Hecke $L$-functions",
  "authors": [
    "Dohyeong Kim"
  ],
  "comment": "59 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove the transfer congruence between $p$-adic Hecke $L$-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer's congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the $q$-expansion principle, and some modification of Hsieh's Whittaker model for Katz' Eisenstein series. As a first application, we prove explicit congruence between special values of Hasse-Weil $L$-function of a CM elliptic curve twisted by Artin representations. As a second application, we prove the existence of a non-commutative $p$-adic $L$-function in the algebraic $K_1$-group of the completed localized Iwasawa algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-05T08:22:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adic hecke",
      "transfer congruence",
      "hilbert modular varieties",
      "hsiehs whittaker model",
      "cm elliptic curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1184K"
    }
  }
}