{
  "id": "2312.05841",
  "version": "v1",
  "published": "2023-12-10T09:51:05.000Z",
  "updated": "2023-12-10T09:51:05.000Z",
  "title": "Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_{n+1} \\times U_{n}$",
  "authors": [
    "Xenia Dimitrakopoulou"
  ],
  "comment": "22 pages; comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "By $p$-adically interpolating the branching law for the spherical pair $(U_n, U_{n+1} \\times U_{n})$ over an imaginary quadratic field, we construct a $p$-adic $L$-function attached to Coleman families of cohomological automorphic representations of $U_{n+1} \\times U_{n}$. Our $p$-adic $L$-function interpolates the square root of the central critical $L$-value. It has weight and anticyclotomic variables and its construction relies on the proof of the unitary Gan--Gross--Prasad conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-10T09:51:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coleman families",
      "imaginary quadratic field",
      "unitary gan-gross-prasad conjecture",
      "cohomological automorphic representations",
      "function interpolates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}