The Selberg trace formula for the Picard group SL(2, Z[i])

DOI10.4064/aa-42-4-391-424zbMath0539.10024OpenAlexW1159993913MaRDI QIDQ3325812

Janusz Szmidt

Publication date: 1983

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/205884

zbMATH Keywords

Selberg trace formulaPicard groupRankin-Selberg method

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Structure of modular groups and generalizations; arithmetic groups (11F06) Fourier coefficients of automorphic forms (11F30) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Automorphic functions in symmetric domains (32N15)

Related Items (10)

Generalized eigenfunctions and eigenvalues: A unifying framework for Shnol-type theorems ⋮ Bounds for eigenforms on arithmetic hyperbolic 3-manifolds ⋮ The character of \(\mathrm{GL}(2)\) automorphic forms ⋮ Prime geodesic theorem for the Picard manifold ⋮ Koecher-Maass series associated to Hermitian modular forms of degree 2 and a characterization of cusp forms by the Hecke bound ⋮ On Kuznetsov-Bykovskii's formula of counting prime geodesics ⋮ Deducing Selberg trace formula via Rankin–Selberg method for 𝐺𝐿₂ ⋮ Note on the Selberg trace formula for the Picard group ⋮ The second moment of symmetric square L-functions over Gaussian integers ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums]

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