{
  "annotation_id": "f76e954a-e95a-4834-81eb-9183f884fc18",
  "date_created": "2026-03-02T18:01:18.009000Z",
  "date_modified": "2026-03-02T18:01:18.009000Z",
  "file_hash": "0bdc64a127964307647d34e63ef9bed83a59a68c7cadb4d0b8b7c48e31680ab2",
  "private": false,
  "record": {
    "abstract": "The spectral test of random number generators (R.R. Coveyou and R.D.\nMcPherson, 1967) is generalized. The sequence of random numbers is analyzed\nexplicitly not just via their n-tupel distributions. The generalized analysis\nof many generators becomes possible due to a theorem on the harmonic analysis\nof multiplicative groups of residue class rings. We find that the mixed\nmultiplicative generator with power of two modulus does not pass the extended\ntest with an ideal result. Best qualities has a new generator with the\nrecursion formula X(k+1)=a*X(k)+c*int(k/2) mod 2^d. We discuss the choice of\nthe parameters a, c for very large moduli 2^d and present an implementation of\nthe suggested generator with d=256, a=2^128+2^64+2^32+62181, c=(2^160+1)*11463.",
    "arxiv_id": "physics/9610003",
    "authors": [
      "Oliver Schnetz"
    ],
    "categories": [
      "physics.comp-ph"
    ],
    "title": "Harmonic analysis of random number generators and multiplicative groups   of residue class rings",
    "url": "https://arxiv.org/abs/physics/9610003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2e594c4b-c51c-4d0d-87c6-fbbe85334b0e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}