Pith Number

pith:M5FXWNZY

pith:2019:M5FXWNZYZFP7GL7X6PTI2FCFP4

not attested not anchored not stored refs pending

On the mean value of the magnitude of an exponential sum involving the divisor function

Mayank Pandey

arxiv:1901.07280 v4 · 2019-01-22 · 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{M5FXWNZYZFP7GL7X6PTI2FCFP4}

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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.

Cited by

1 paper in Pith

Moment estimates for the exponential sum with higher divisor functions

Receipt and verification

First computed	2026-07-05T01:03:18.700061Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

674b7b3738c95ff32ff7f3e68d14457f2c7d0b63413847c8ff91fb7e83873fd5

Aliases

arxiv: 1901.07280 · arxiv_version: 1901.07280v4 · doi: 10.48550/arxiv.1901.07280 · pith_short_12: M5FXWNZYZFP7 · pith_short_16: M5FXWNZYZFP7GL7X · pith_short_8: M5FXWNZY

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/M5FXWNZYZFP7GL7X6PTI2FCFP4 \
  | 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: 674b7b3738c95ff32ff7f3e68d14457f2c7d0b63413847c8ff91fb7e83873fd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e31b95a8de14f6c58a6257b62d42ffb94e5a4ed903c04d683f2663f2c87d03aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-01-22T12:14:03Z",
    "title_canon_sha256": "97dde76af6a9684fb505575746dce53248bd46b859ed57eae3156c215ce91c8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.07280",
    "kind": "arxiv",
    "version": 4
  }
}