Pith Number

pith:DM5EPN4J

pith:2026:DM5EPN4JGLSB4Z5YPAVZNNS5A5

not attested not anchored not stored refs resolved

Explicit Formulas for the Casimir Eigenvalues of $SL(n,\mathbb{Z})$-Maass Forms

Vishal Muthuvel

Maass forms for SL(n,Z) have their Casimir eigenvalues given explicitly by formulas in the Langlands parameters.

arxiv:2605.16803 v1 · 2026-05-16 · math.NT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DM5EPN4JGLSB4Z5YPAVZNNS5A5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

For any 1 ≤ m ≤ n and Maass form φ for SL(n,Z), we provide a formula for the eigenvalue of D_{m,n} associated with φ in terms of the Langlands parameters of φ.

C2weakest assumption

The Maass forms for SL(n,Z) are eigenfunctions of the full set of Casimir operators D_{m,n} of orders 1 ≤ m ≤ n for GL(n,R), and the Langlands parameters are the standard ones that classify these forms.

C3one line summary

Explicit formulas are derived for the eigenvalues of Casimir operators D_{m,n} on SL(n,Z)-Maass forms in terms of Langlands parameters, with a graph-theoretic proof that recovers the known Laplacian case for m=2.

References

3 extracted · 3 resolved · 0 Pith anchors

[1] Eisenstein Series and the Trace Formula 1979

[2] On some applications of the universal en- veloping algebra of a semisimple Lie algebra 1951

[3] Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series 1956

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:23.006773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1b3a47b78932e41e67b8782b96b65d07597d1918caf7dca86eebce13b69154c5

Aliases

arxiv: 2605.16803 · arxiv_version: 2605.16803v1 · doi: 10.48550/arxiv.2605.16803 · pith_short_12: DM5EPN4JGLSB · pith_short_16: DM5EPN4JGLSB4Z5Y · pith_short_8: DM5EPN4J

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/DM5EPN4JGLSB4Z5YPAVZNNS5A5 \
  | 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: 1b3a47b78932e41e67b8782b96b65d07597d1918caf7dca86eebce13b69154c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3244df05aca0af754224ca731421784d0e91c9a133cfcdf8e4c8dea61baefcc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-16T04:15:50Z",
    "title_canon_sha256": "a02cd7c334b8664ee936cc70c21e7811717286a80c5a944e2b1214054ea65be4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16803",
    "kind": "arxiv",
    "version": 1
  }
}