Pith Number

pith:EEJLS36G

pith:2026:EEJLS36GOAF6PVABAF6TGHWTQZ

not attested not anchored not stored refs resolved

On Average Modulus of Random Polynomials Over a Unit Circle and Disc

Mohd.Ibrahim Mir, Sajad A. Sheikh

Random polynomials with i.i.d. standard normal coefficients have their average modulus on the unit circle and disk newly characterized, with maximum-modulus tail probabilities bounded by Markov inequality.

arxiv:2605.17386 v1 · 2026-05-17 · math.CV

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\pithnumber{EEJLS36GOAF6PVABAF6TGHWTQZ}

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Claims

C1strongest claim

The article presents new results concerning the average modulus of random polynomials on the unit circle and the unit disc with coefficients distributed as standard normal variates, together with bounds on the maximum modulus for Gaussian and uniform coefficients obtained via Markov inequality.

C2weakest assumption

The coefficients of the polynomials are independent and identically distributed as standard normal, Gaussian, or uniform random variables, and the evaluations are restricted to the unit circle and closed unit disk.

C3one line summary

Computes average modulus of random polynomials with normal coefficients on unit circle and disk and derives Markov inequality bounds on maximum modulus for Gaussian and uniform coefficients.

References

29 extracted · 29 resolved · 1 Pith anchors

[1] Analytic Theory of Polynomials: Critical Points, Zeros and Extremal Properties 2002

[2] Polynomials and polynomial inequalities 1995

[3] Random polynomials 1986

[4] Topics in polynomials: extremal prop- erties, inequalities, zeros 1994

[5] A Probabilistic Version of Enestr¨ om–Kakeya Theorem for Certain Random Polynomials, 2023 · doi:10.3390/math11194061

Receipt and verification

First computed	2026-05-20T00:03:55.948101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2112b96fc6700be7d401017d331ed3865ad8df4af829c53123a627070a26ea4c

Aliases

arxiv: 2605.17386 · arxiv_version: 2605.17386v1 · doi: 10.48550/arxiv.2605.17386 · pith_short_12: EEJLS36GOAF6 · pith_short_16: EEJLS36GOAF6PVAB · pith_short_8: EEJLS36G

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EEJLS36GOAF6PVABAF6TGHWTQZ \
  | 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: 2112b96fc6700be7d401017d331ed3865ad8df4af829c53123a627070a26ea4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b3f2dcff2852a1b4108916d8991d7aa8d084db8c3f1ba76e6324de2f536d8bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-05-17T11:09:06Z",
    "title_canon_sha256": "95c76061b3e7b9896ca052e7f23a75c6829e3a962998d203101e3062fd55db27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17386",
    "kind": "arxiv",
    "version": 1
  }
}