Pith Number

pith:PNSIUUII

pith:2026:PNSIUUIIFOYFJAMWSGEJ2M7HGS

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Joint Sato-Tate Laws for Transformations of Hecke Eigenvalues: The Vertical Case

Mohammad H. Hamdar, Tian Wang

A framework combining a higher-dimensional Erdős-Turán analogue with Hardy-Krause variation approximations delivers effective joint Sato-Tate laws for Hecke eigenvalues and Frobenius traces.

arxiv:2604.24753 v2 · 2026-04-27 · math.NT

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\pithnumber{PNSIUUIIFOYFJAMWSGEJ2M7HGS}

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Record completeness

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4 Citations 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 obtain novel results concerning the distribution of arithmetic relations, and, more generally, multi-dimensional functions of Fourier coefficients and Frobenius traces.

C2weakest assumption

That a broad class of relevant functions can be approximated by functions of bounded Hardy-Krause variation and that the higher-dimensional μ-analogue of the Erdős-Turán inequality applies with effective error terms to the vertical Sato-Tate problems.

C3one line summary

A new analytic framework establishes joint Sato-Tate laws with effective errors for transformations of Hecke eigenvalues in the vertical case for cusp forms and elliptic curves.

Receipt and verification

First computed	2026-06-09T02:08:43.074249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b648a51082bb054819691889d33e734a9c77bc9772b3de9d76836bca954c21a

Aliases

arxiv: 2604.24753 · arxiv_version: 2604.24753v2 · doi: 10.48550/arxiv.2604.24753 · pith_short_12: PNSIUUIIFOYF · pith_short_16: PNSIUUIIFOYFJAMW · pith_short_8: PNSIUUII

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/PNSIUUIIFOYFJAMWSGEJ2M7HGS \
  | 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: 7b648a51082bb054819691889d33e734a9c77bc9772b3de9d76836bca954c21a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "023e1a479b0a785eb0a26659dffc9dac4992e64c147cd6a8c421ce812a39a93c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-04-27T17:55:14Z",
    "title_canon_sha256": "daa54b55460dd6d480b14e0f804986fb7b5a30704cac6f2266d38410a1a0fe04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.24753",
    "kind": "arxiv",
    "version": 2
  }
}