Pith Number

pith:GEZ2L5PC

pith:2019:GEZ2L5PCLMRIPSRGJPCWTKR6N2

not attested not anchored not stored refs pending

On the mean value of the generalized Dirichlet L-functions with the weight of the Gauss Sums

Rong Ma, Yana Niu

arxiv:1912.13153 v1 · 2019-12-31 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GEZ2L5PCLMRIPSRGJPCWTKR6N2}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T00:29:06.495285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3133a5f5e25b2287ca264bc569aa3e6e87177fc681bf000ce4cdb41af38c4ee1

Aliases

arxiv: 1912.13153 · arxiv_version: 1912.13153v1 · doi: 10.48550/arxiv.1912.13153 · pith_short_12: GEZ2L5PCLMRI · pith_short_16: GEZ2L5PCLMRIPSRG · pith_short_8: GEZ2L5PC

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GEZ2L5PCLMRIPSRGJPCWTKR6N2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3133a5f5e25b2287ca264bc569aa3e6e87177fc681bf000ce4cdb41af38c4ee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07f443ebf0259f88822c56a7339c7ddaa244ff08ca25069e493420685a702738",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-12-31T03:13:09Z",
    "title_canon_sha256": "715c5373bd1d12291c27084b86735d9eb9080f6375ae555bd7fb622c6cfa6a8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.13153",
    "kind": "arxiv",
    "version": 1
  }
}