{
  "abstract": "We describe a new family of Dirichlet L-functions that provably have an unusual value distribution. Experimentally, we find that the L-functions in this family have a significant and previously undetected bias in the distribution of gaps between their zeros. These phenomena appear to have an arithmetic explanation that corresponds to the nonvanishing of a certain Gauss-type sum. We give a complete classification of the characters for which this sum is nonzero and count them. This sum vanishes for 100% of primitive Dirichlet characters, so L-functions in our newly discovered family are rare (a set of density zero among all primitive characters). The nonvanishing of this sum implies that there is a main term when one integrates the Z-function associated to a Dirichlet L-function over a long interval. We prove that the L-functions in this family are the only GL(1)/Q or GL(2)/Q cuspidal automorphic L-functions whose Z-functions have a \"large\" mean value when integrated. We discuss analogous results for the Riemann zeta-function.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31744",
  "author_total": 3,
  "authors": [
    {
      "name": "Jonathan W. Bober"
    },
    {
      "name": "Zhenchao Ge"
    },
    {
      "name": "Micah B. Milinovich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9040pk5a7sdhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31744",
  "fulltext_url": null,
  "id": "9040pk5a7sdhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31744",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223691712",
  "pdf_url": "https://arxiv.org/pdf/2610.31744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9040pk5a7sdhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Biases in gaps between zeros of Dirichlet L-functions",
  "title_text": "Biases in gaps between zeros of Dirichlet L-functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/9040pk5a7sdhz",
  "venue": "arXiv",
  "versions": []
}