Pith Number

pith:H27E6O2B

pith:2026:H27E6O2BCJQ4WNYSD5ZWZHJ4RA

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Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Reduction

Yao Cheng

Non-vanishing of newform spaces for supercuspidals implies the same for all generic representations of p-adic SO(2n+1).

arxiv:2605.15678 v1 · 2026-05-15 · math.RT · math.NT

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\pithnumber{H27E6O2BCJQ4WNYSD5ZWZHJ4RA}

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Claims

C1strongest claim

We prove that if the space of newforms is non-zero for every irreducible generic supercuspidal representation of SO_{2n+1} then it is also non-zero for all irreducible generic representations of SO_{2n+1}.

C2weakest assumption

The definitions and standard properties of newforms and generic representations for p-adic SO(2n+1) as used in the reduction steps, which are invoked to extend the supercuspidal case to the general case.

C3one line summary

Proves that if newform spaces are non-zero for all irreducible generic supercuspidal representations of SO(2n+1), then they are non-zero for all irreducible generic representations.

References

51 extracted · 51 resolved · 1 Pith anchors

[1] J. Arthur. The endoscopic classification of representations: Orthogonal and symplectic groups , volume 61 of American Mathematical Society Colloquium Publications . American Mathematical Society, Prov 2013

[2] H. Atobe. Jacquet modules and local Langlands correspondence . Inventiones Mathematiace , 219:831--871, 2020 2020

[3] Atobe, The set of local A-packets containing a given representation , Journal für die reine und angewandte Mathematik , vol 2023

[4] H. Atobe. Local newforms for generic representations of unramified even unitary groups I: Even conductor case . Forum of Mathematics, Sigma , 13(23):1--32, 2025 2025

[5] H. Atobe, W. T. Gan, A. Ichino, T. Kaletha, A. M\' i nguez, and S. W. Shin. Local intertwining relations and co-tempered A -packets of classical groups . arXiv:2410.13504v1 , 2024 2024

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Receipt and verification

First computed	2026-05-20T00:01:11.954111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ebe4f3b411261cb37121f736c9d3c8810b9ce975d64715c255cf093030c4722

Aliases

arxiv: 2605.15678 · arxiv_version: 2605.15678v1 · doi: 10.48550/arxiv.2605.15678 · pith_short_12: H27E6O2BCJQ4 · pith_short_16: H27E6O2BCJQ4WNYS · pith_short_8: H27E6O2B

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/H27E6O2BCJQ4WNYSD5ZWZHJ4RA \
  | 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: 3ebe4f3b411261cb37121f736c9d3c8810b9ce975d64715c255cf093030c4722

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecb2aada5e83c30c7426665245f032a040746494c859a01841ac50d014406425",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-05-15T07:00:01Z",
    "title_canon_sha256": "ee908c68e3970adb604e88c06911a522cb74bf698cf00c61af0bc2d4a8db2c2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15678",
    "kind": "arxiv",
    "version": 1
  }
}