Pith Number

pith:6GWKTRIK

pith:2026:6GWKTRIKC7NGO3UHZEAID6DPAP

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Lacunary recurrences and 2-adic properties of Eisenstein series

Andrei Jorza, Liubomir Chiriac

The minimal 2-adic valuation of coefficients in Eisenstein series expressed as polynomials in G4 and G6 is given exactly by the binary expansion of the weight.

arxiv:2605.09738 v2 · 2026-05-10 · math.NT

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\pithnumber{6GWKTRIKC7NGO3UHZEAID6DPAP}

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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 prove a recent conjecture giving an exact formula for the minimal 2-adic valuation of these coefficients in terms of the binary expansion of the weight.

C2weakest assumption

The lacunary recurrences for Eisenstein series exist and can be manipulated to derive the precise valuation formula without additional hidden conditions on the weight.

C3one line summary

Proves exact formula for minimal 2-adic valuation of coefficients in G_k expressed as polynomial in G4 and G6, given by binary expansion of the weight k.

Receipt and verification

First computed	2026-06-03T01:05:51.181351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1aca9c50a17da676e87c90081f86f03e74f2300044f4da6472598f9892eb7d4

Aliases

arxiv: 2605.09738 · arxiv_version: 2605.09738v2 · doi: 10.48550/arxiv.2605.09738 · pith_short_12: 6GWKTRIKC7NG · pith_short_16: 6GWKTRIKC7NGO3UH · pith_short_8: 6GWKTRIK

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6GWKTRIKC7NGO3UHZEAID6DPAP \
  | 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: f1aca9c50a17da676e87c90081f86f03e74f2300044f4da6472598f9892eb7d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8f58a878d9fdf17ff8d7989b9b1cf74f13b80ea42b1c7670942b9418cb889a8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-10T20:17:15Z",
    "title_canon_sha256": "d9c55ab22cdb1696c3c55fa5d36c6e9d941feaf0dbb0b20552e07d137b3c8200"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09738",
    "kind": "arxiv",
    "version": 2
  }
}