Pith Number

pith:VW6JV23U

pith:2025:VW6JV23UD5O53S4HZCSUTPZPXC

not attested not anchored not stored refs pending

Character sums to prime power moduli evaluated at binary quadratic forms

Aishik Chattopadhyay, Stephan Baier

Short character sums to prime power moduli evaluated at binary quadratic forms admit explicit estimates.

arxiv:2508.11231 v3 · 2025-08-15 · math.NT

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\usepackage{pith}
\pithnumber{VW6JV23UD5O53S4HZCSUTPZPXC}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms.

C2weakest assumption

The p-adic theory of exponential sums initiated by Milićević applies directly and without major additional restrictions to the evaluation at binary quadratic forms for prime power moduli.

C3one line summary

Derives estimates for character sums to prime power moduli at binary quadratic forms, complementing Heath-Brown via p-adic methods initiated by Milićević.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:01:35.114958Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adbc9aeb741f5dddcb87c8a549bf2fb88ef3f968e074f6357471b9fe58d7c453

Aliases

arxiv: 2508.11231 · arxiv_version: 2508.11231v3 · doi: 10.48550/arxiv.2508.11231 · pith_short_12: VW6JV23UD5O5 · pith_short_16: VW6JV23UD5O53S4H · pith_short_8: VW6JV23U

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/VW6JV23UD5O53S4HZCSUTPZPXC \
  | 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: adbc9aeb741f5dddcb87c8a549bf2fb88ef3f968e074f6357471b9fe58d7c453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c74bbece846bf4cebdb62d9071f9a6138e356afb8142512b9bf4906844750cdf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-08-15T05:43:27Z",
    "title_canon_sha256": "336ebcbfcbab069527716984ee7ebedb3d59144a5aa37ca6d520466799a24b00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.11231",
    "kind": "arxiv",
    "version": 3
  }
}