Pith Number

pith:NMGW7YO7

pith:2026:NMGW7YO7U6JRNMUGYM6GITMKOQ

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Statistically characterized subgroups related to arithmetic-type sequence of integers

Ayan Ghosh, Pratulananda Das, Tamim Aziz

Statistically characterized subgroups for a broader class of arithmetic-type sequences recover all prior cardinality results as special cases but exhibit distinct behavior.

arxiv:2605.16577 v1 · 2026-05-15 · math.GR

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Record completeness

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4 Citations open

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Claims

C1strongest claim

All previously obtained cardinality related observations for statistically characterized subgroups corresponding to arithmetic sequences as well as certain non-arithmetic sequences follow as special cases of our results. Moreover, we show that this broader class exhibits drastically different behavior and differs significantly from the previously studied special cases.

C2weakest assumption

The paper assumes that the statistical characterization extends coherently to the broader class of arithmetic-type sequences without requiring new restrictions or producing contradictions with the special cases already studied.

C3one line summary

Authors extend statistical subgroup characterizations to a broad class of arithmetic-type sequences, recovering earlier cardinality results as special cases while noting new qualitative differences.

References

41 extracted · 41 resolved · 0 Pith anchors

[1] Arbault, Sur l’ensemble de convergence absolue d’une s´ erie trigonom´ etrique., Bull 1952

[2] A. Arhangel’skii , M. Tkachenko, Topological Groups and Related Structures: An Introduc- tion to Topological Algebra, Atlantis Press, Paris, 2008 2008

[3] L. Außenhofer, D. Dikranjan, Locally quasi-convex compatible topologies on locally compact abelian groups, Mathematische Zeitschrift, 296 (2020), 325-351 2020

[4] G. Barbieri, D. Dikranjan, A. Giordano Bruno, H. Weber, Dirichlet sets vs characterized subgroups, Topol. Appl. 231, 50–76 (2017) 2017

[5] M. Balcerzak, K. Dems, A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, J. Math. Anal. Appl., 328(1) (2007), 715–729 2007

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:30.637281Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b0d6fe1dfa79316b286c33c644d8a740eb5d5251bd6bdde2ba21dc47f202ac3

Aliases

arxiv: 2605.16577 · arxiv_version: 2605.16577v1 · doi: 10.48550/arxiv.2605.16577 · pith_short_12: NMGW7YO7U6JR · pith_short_16: NMGW7YO7U6JRNMUG · pith_short_8: NMGW7YO7

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NMGW7YO7U6JRNMUGYM6GITMKOQ \
  | 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: 6b0d6fe1dfa79316b286c33c644d8a740eb5d5251bd6bdde2ba21dc47f202ac3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb30d0d28a21c6253887be6c92e7c808fae47c2a4c2174a61b9d7a04e072262e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-15T19:32:26Z",
    "title_canon_sha256": "5b4b56eefeac400f6e48c635e3503cd27337c2307bb3513385a738ba8b21f245"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16577",
    "kind": "arxiv",
    "version": 1
  }
}