{
  "id": "2111.15287",
  "version": "v2",
  "published": "2021-11-30T11:08:50.000Z",
  "updated": "2022-10-14T06:01:13.000Z",
  "title": "Ramanujan-style congruences for prime level",
  "authors": [
    "Arvind Kumar",
    "Moni Kumari",
    "Pieter Moree",
    "Sujeet Kumar Singh"
  ],
  "comment": "The final version, published in Mathematische Zeitschriften",
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish Ramanujan-style congruences modulo certain primes $\\ell$ between an Eisenstein series of weight $k$, prime level $p$ and a cuspidal newform in the $\\varepsilon$-eigenspace of the Atkin-Lehner operator inside the space of cusp forms of weight $k$ for $\\Gamma_0(p)$. Under a mild assumption, this refines a result of Gaba-Popa. We use these congruences and recent work of Ciolan, Languasco and the third author on Euler-Kronecker constants, to quantify the non-divisibility of the Fourier coefficients involved by $\\ell.$ The degree of the number field generated by these coefficients we investigate using recent results on prime factors of shifted prime numbers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-10-14T06:01:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F11",
      "11F80",
      "11N37"
    ],
    "keywords": [
      "prime level",
      "establish ramanujan-style congruences modulo",
      "atkin-lehner operator inside",
      "shifted prime numbers",
      "prime factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}