Pith Number

pith:AQCMB7UM

pith:2026:AQCMB7UMTNGIT6NY5GXV2LHJRH

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Elasticity of Orders from the $S$-relative Davenport Constant: an Arithmetic Application of a Number-Theoretic Investigation

Grant Moles, Jared Kettinger

The S-relative Davenport constant determines the elasticity of non-integrally closed orders when the conductor is prime or primary.

arxiv:2605.17595 v1 · 2026-05-17 · math.AC

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Claims

C1strongest claim

We show that this related invariant is the exact tool needed to tackle the question of elasticity in non-integrally closed orders.

C2weakest assumption

The conductor ideal I = (O : O_K) is prime as an ideal of O or primary for orders in quadratic number fields.

C3one line summary

Develops the S-relative Davenport constant as a tool to determine elasticity of orders with prime or primary conductor ideals in algebraic number fields.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] Davenport constant with weights and some related ques- tions.Integers, 6:A30, 2006 2006

[2] Safia Boukheche, Kamil Merito, Oscar Ordaz, and Wolfgang A Schmid. Monoids of sequences over finite abelian groups defined via zero-sums with respect to a given set of weights and applications to fact 2022

[3] Conditions for a zero sum modulo n.Canadian Mathematical Bulletin, 18(1):27–29, 1975 1975

[4] Overrings of half-factorial orders 2026

[5] The conductor ideal of an order.Expository Paper, 2019.https://kconrad.math.uconn 2019

Receipt and verification

First computed	2026-05-20T00:04:47.747545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0404c0fe8c9b4c89f9b8e9af5d2ce989f87f66574e80a724473559c8fdd28ab2

Aliases

arxiv: 2605.17595 · arxiv_version: 2605.17595v1 · doi: 10.48550/arxiv.2605.17595 · pith_short_12: AQCMB7UMTNGI · pith_short_16: AQCMB7UMTNGIT6NY · pith_short_8: AQCMB7UM

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AQCMB7UMTNGIT6NY5GXV2LHJRH \
  | 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: 0404c0fe8c9b4c89f9b8e9af5d2ce989f87f66574e80a724473559c8fdd28ab2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6053877285a225159b2a20038404e5326565c35283ccb7b5610d7c5fa79742e7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-05-17T18:46:21Z",
    "title_canon_sha256": "d5394b1d23dd044d8e4ad110b882b0912516c9a1e4b1ca7334ed55fca6a77261"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17595",
    "kind": "arxiv",
    "version": 1
  }
}