Pith Number

pith:BBVPMA2Q

pith:2026:BBVPMA2QDMW5K6LTC7QVZPOE7M

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Multiplicative Diophantine approximation and bounds for lattice sums

M.M.Skriganov

Lattice sums arising in integer point counting inside polyhedra admit upper bounds from multiplicative Diophantine approximation.

arxiv:2605.13640 v1 · 2026-05-13 · math.CO

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

We estimate the lattice sums arising in the context of the integer point counting in polyhedra.

C2weakest assumption

That the lattice sums admit useful upper bounds derived from multiplicative Diophantine approximation without further restrictions on the polyhedra or the lattice that are stated in the abstract.

C3one line summary

Estimates lattice sums for integer point counting in polyhedra via multiplicative Diophantine approximation.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] J.W.S.Cassels,An introduction to the geometry of numbers, Springer Verlag, Berlin, 1959 1959

[2] P.M.Gruber, C.G.Lekkerkerker,Geometry of numbers, North–Holland Math. Libraey, vol. 37, Elsevier Sci. Pub., Amsterdam, 1987 1987

[3] R.A.Meyers), Springer, New York, 2011 2011

[4] L.Kuipers, H.Niederreiter,Uniform distribution of sequences, John Wiley & Sons, N.Y., 1974 1974

[5] G.A.Margulis,Diophantine approximation, lattices and flows on homogeneous spaces, in A panorama of number theory or the view from Baker’s garden (Ed. G.W¨ ustholz), pp. 280–310, Cambridge Univ. Press, 2002

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Integer points in a simplex and related Diophantine problems: Hardy--Littlewood asymptotics in higher dimensions

Receipt and verification

First computed	2026-05-18T02:44:17.616594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

086af603501b2dd5797317e15cbdc4fb2689502c4d2279606bce149d6d4ffa7f

Aliases

arxiv: 2605.13640 · arxiv_version: 2605.13640v1 · doi: 10.48550/arxiv.2605.13640 · pith_short_12: BBVPMA2QDMW5 · pith_short_16: BBVPMA2QDMW5K6LT · pith_short_8: BBVPMA2Q

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BBVPMA2QDMW5K6LTC7QVZPOE7M \
  | 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: 086af603501b2dd5797317e15cbdc4fb2689502c4d2279606bce149d6d4ffa7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "728e8908a3cdee141778d88982196b263c4b1630012a2383ce9497ac0d367295",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T15:05:12Z",
    "title_canon_sha256": "444509b9051253ad17813017d8fabfc8b61d8b29e1972afefd5a253f23931dbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13640",
    "kind": "arxiv",
    "version": 1
  }
}