A spectral reciprocity formula and non-vanishing for \(L\)-functions on \(\mathrm{GL}(4)\times\mathrm{GL}(2)\)

DOI10.1016/j.jnt.2019.05.011zbMath1506.11078arXiv1705.04344OpenAlexW2963051045MaRDI QIDQ2322894

Yanyan Li

Publication date: 5 September 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.04344

zbMATH Keywords

momentsRankin-Selberg \(L\)-functionsVoronoi summationnon-vanishingKuznetsov formulaspectral summation

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (13)

Subconvexity bounds for twisted 𝐿-functions, II ⋮ The variance of closed geodesics in balls and annuli on the modular surface ⋮ Parametrization of Kloosterman sets and \(\mathrm{SL}_3\)-Kloosterman sums ⋮ The Weyl bound for triple product \(L\)-functions ⋮ Spectral reciprocity via integral representations ⋮ An explicit formula for the second moment of Maass form symmetric square \(L\)-functions ⋮ A Voronoi summation formula for non-holomorphic Maass forms of half-integral weight ⋮ The Relative Trace Formula in Analytic Number Theory ⋮ On the random wave conjecture for dihedral Maaß forms ⋮ The triple reciprocity law for the twisted second moments of Dirichlet $L$-functions over function fields ⋮ On the balanced Voronoï formula for \(\mathrm{GL}_N\) ⋮ Voronoï summation for GLn: collusion between level and modulus ⋮ Motohashi’s formula for the fourth moment of individual DirichletL-functions and applications

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