Generalized Ramanujan conjecture over general imaginary quadratic fields

DOI10.1515/form.2011.050zbMath1257.11052OpenAlexW1979810873WikidataQ122972222 ScholiaQ122972222MaRDI QIDQ2882747

Maki Nakasuji

Publication date: 7 May 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/form.2011.050

zbMATH Keywords

imaginary quadratic fieldssymmetric square \(L\)-functiongeneralized Ramanujan conjectureRamanujan-Selberg conjecture

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (9)

Effective estimates on integral quadratic forms: Masser's conjecture, generators of orthogonal groups, and bounds in reduction theory ⋮ Non-vanishing of special \(L\)-values of cusp forms on GL(2) with totally split prime power twists ⋮ On the Ramanujan conjecture over number fields ⋮ Bianchi modular symbols and \(p\)-adic \(L\)-functions ⋮ A note on the zeros of zeta and \(L\)-functions ⋮ Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds ⋮ The role of the Ramanujan conjecture in analytic number theory ⋮ On Kuznetsov-Bykovskii's formula of counting prime geodesics ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums]

Cites Work

• Nonvanishing of \(L\)-functions for \(\mathrm{GL}(2)\)
• Cuspidality of symmetric powers with applications.
• On Selberg's eigenvalue conjecture
• Zeros of principal \(L\)-functions and random matrix theory
• On Euler Products and the Classification of Automorphic Representations I
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂

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