{
  "id": "1608.03014",
  "version": "v1",
  "published": "2016-08-10T00:45:38.000Z",
  "updated": "2016-08-10T00:45:38.000Z",
  "title": "Some sums over irreducible polynomials",
  "authors": [
    "David E Speyer"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We prove a number of conjectures due to Dinesh Thakur concerning sums of the form $\\sum_P h(P)$ where the sum is over monic irreducible polynomials $P$ in $\\mathbb{F}_q[T]$, the function $h$ is a rational function and the sum is considered in the $T^{-1}$-adic topology. As an example of our results, in $\\mathbb{F}_2[T]$, the sum $\\sum_P \\tfrac{1}{P^k - 1}$ always converges to a rational function, and is $0$ for $k=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-10T00:45:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational function",
      "dinesh thakur concerning sums",
      "monic irreducible polynomials",
      "adic topology",
      "conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}