Pith Number

pith:W5RAJ4XL

pith:2026:W5RAJ4XLER4AMU2PG7H7N734GC

not attested not anchored not stored refs resolved

Hecke Eigenvalues of Ikeda Lifts

Ameya Pitale, Nagarjuna Chary Addanki

Hecke eigenvalues of Ikeda lifts are positive for all sufficiently large primes.

arxiv:2605.16083 v1 · 2026-05-15 · math.NT

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\pithnumber{W5RAJ4XLER4AMU2PG7H7N734GC}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

λ_F(p^r) can be written as a polynomial in p^{±1/2} with a positive leading term; the coefficients of this polynomial are bounded, and therefore λ_F(p^r) is positive for all sufficiently large primes p.

C2weakest assumption

The spherical map for the Hecke algebra of the symplectic group correctly transfers the Hecke eigenvalues from the Ikeda lift to an explicit algebraic expression that can be analyzed as a polynomial.

C3one line summary

Derives explicit formula for Hecke eigenvalues of Ikeda lifts as polynomials in p^{±1/2} with bounded coefficients and proves positivity for large primes.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] N. C. Addanki. On signs of eigenvalues of Siegel modular forms satisfying Ramanujan conjec- ture.arXiv, 2024 2024

[2] N. C. Addanki. On signs of Hecke eigenvalues of Ikeda lifts.Ramanujan J., 66(4):81, 2025 2025

[3] Andrianov.Introduction to Siegel modular forms and Dirichlet series 2009

[4] A. N. Andrianov. Spherical functions forGLn over local fields, and the summation of Hecke series.Mat. Sb. (N.S.), 83(125):429–451, 1970 1970

[5] A. N. Andrianov. Euler products that correspond to Siegel’s modular forms of genus2.Uspehi Mat. Nauk, 29(3(177)):43–110, 1974 1974

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:51.929799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b76204f2eb247806534f37cff6ff7c30872cd2443d13e2346210340d97cc4744

Aliases

arxiv: 2605.16083 · arxiv_version: 2605.16083v1 · doi: 10.48550/arxiv.2605.16083 · pith_short_12: W5RAJ4XLER4A · pith_short_16: W5RAJ4XLER4AMU2P · pith_short_8: W5RAJ4XL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W5RAJ4XLER4AMU2PG7H7N734GC \
  | 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: b76204f2eb247806534f37cff6ff7c30872cd2443d13e2346210340d97cc4744

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1615ce6da5d2862c6a6f42a4ba89f036dfc3a5ceb85856676f999aee3bd91f1",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-15T15:45:08Z",
    "title_canon_sha256": "0dc1403946d6dc425c0573a5b0d25569406bd68800f0c4d94f160764a323623c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16083",
    "kind": "arxiv",
    "version": 1
  }
}