Pith Number

pith:XDNXJSRA

pith:2026:XDNXJSRAND27QX6V4OIIQ6PBRJ

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A Weyl-type theorem for Diophantine approximations driven by LCA groups and applications

Aihua Fan

Every action of a locally compact Abelian group on the torus decomposes into uniquely ergodic subsystems.

arxiv:2605.15580 v1 · 2026-05-15 · math.DS · math.CA · math.NT

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Claims

C1strongest claim

Every action of a locally compact Abelian group on the torus admits a decomposition into uniquely ergodic subsystems, yielding a Weyl-type equidistribution theorem.

C2weakest assumption

The proof relies on a pre-existing characterization of unique ergodicity for amenable group actions on compact metric spaces; if this characterization fails to apply to the specific LCA actions considered here, the decomposition result does not follow.

C3one line summary

Establishes a decomposition of LCA group actions on the torus into uniquely ergodic subsystems, with applications to Bohr orthogonality and Wiener-type theorems on LCA groups.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] L. Amerio and G. Prouse,Almost periodic functions and functional equations, Van Nostrand, New York, 1971 1971

[2] Bass,Suites uniform´ ement denses, moyennes trigonom´ etriques, fonctions pseudo-al´ eatoires, Bull 1959

[3] B. Baake and U. Grimm,Aperiodic Order: Volume 1, A Mathematical Invitation, Cambridge University Press, 2013 2013

[4] A. S. Besicovitch,Almost periodic functions, Dover Publications, 1954 1954

[5] Billingsley,Convergence of probability measures, John Wiley & Sons, New York, 1999 1999

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:06.465726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8db74ca2068f5f85fd5e3908879e18a5fa48f70e9ecfcf93f7a0a0fc6c40240

Aliases

arxiv: 2605.15580 · arxiv_version: 2605.15580v1 · doi: 10.48550/arxiv.2605.15580 · pith_short_12: XDNXJSRAND27 · pith_short_16: XDNXJSRAND27QX6V · pith_short_8: XDNXJSRA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XDNXJSRAND27QX6V4OIIQ6PBRJ \
  | 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: b8db74ca2068f5f85fd5e3908879e18a5fa48f70e9ecfcf93f7a0a0fc6c40240

Canonical record JSON

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    "abstract_canon_sha256": "41759a7dd32aad1b2ddb3832d9ceb7b0dd10172810b98a8c8f3164519054eb99",
    "cross_cats_sorted": [
      "math.CA",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T03:44:30Z",
    "title_canon_sha256": "f8d87aed3c0b0990724867a589d7f9c2deb975e62d5f37e7102d95a2af4e6ffd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15580",
    "kind": "arxiv",
    "version": 1
  }
}