Pith Number

pith:TMHRUEG6

pith:2026:TMHRUEG6DSNWS6WJ6GEOAM426V

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A proof of $p$-adic Gross--Zagier theorem via BDP formula

K\^az{\i}m B\"uy\"ukboduk, Peter Neamti

A wall-crossing argument using the BDP formula proves the p-adic Gross-Zagier theorem for both ordinary and non-ordinary cuspidal forms.

arxiv:2604.13854 v2 · 2026-04-15 · math.NT

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Claims

C1strongest claim

This paper provides a new proof of the p-adic Gross--Zagier formula for the p-adic L-function associated with the base change of a normalised cuspidal eigen-newform f of weight k >= 2 (and families of such) to an imaginary quadratic field K, encompassing classical p-ordinary cases and non-ordinary scenarios including k > 2 and ord_p(a_p(f)) > 0.

C2weakest assumption

The wall-crossing strategy centred on the BDP formula and the theory of Beilinson--Flach elements successfully extends to the non-ordinary cases and higher weights without requiring the traditional comparison of geometric and analytic kernels.

C3one line summary

A new proof of the p-adic Gross-Zagier formula is established via a wall-crossing strategy centered on the BDP formula and Beilinson-Flach elements, covering ordinary and non-ordinary cases for weight k >= 2 and families.

Receipt and verification

First computed	2026-07-24T01:24:11.205067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b0f1a10de1c9b697ac9f188e0339af55dec32af48bf447757d7f2348aa1e283

Aliases

arxiv: 2604.13854 · arxiv_version: 2604.13854v2 · doi: 10.48550/arxiv.2604.13854 · pith_short_12: TMHRUEG6DSNW · pith_short_16: TMHRUEG6DSNWS6WJ · pith_short_8: TMHRUEG6

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TMHRUEG6DSNWS6WJ6GEOAM426V \
  | 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: 9b0f1a10de1c9b697ac9f188e0339af55dec32af48bf447757d7f2348aa1e283

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e4a0a45323bbbe795d3010462f5fcc117ff85525d2e7fcad4ac8fb26b5bf820",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-04-15T13:24:06Z",
    "title_canon_sha256": "fcc74897e5aad72636732e72326adea033b5166f4b1f8346c9751396143bc5e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.13854",
    "kind": "arxiv",
    "version": 2
  }
}