Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms

DOI10.1090/S0894-0347-07-00581-4zbMath1188.11024arXivmath/0509077WikidataQ126176919 ScholiaQ126176919MaRDI QIDQ5441370

Andre Reznikov

Publication date: 12 February 2008

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509077

zbMATH Keywords

Gelfand pairsubconvexitymultiplicity onebounds on Fourier coefficientsperiod of an automorphic formRankin-Selberg identity

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) 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) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (16)

Rankin-Selberg periods for spherical principal series ⋮ On Twisted Gelfand Pairs Through Commutativity of a Hecke Algebra ⋮ Voronoï summation via switching cusps ⋮ Sparse equidistribution problems, period bounds and subconvexity ⋮ On the size of Ikeda lifts ⋮ The subconvexity problem for \(\mathrm{GL}_2\) ⋮ A duality relation for certain triple products of automorphic forms ⋮ Non-vanishing of Taylor coefficients and Poincaré series ⋮ Subconvexity bounds for triple \(L\)-functions and representation theory ⋮ Geodesic restrictions for the Casimir operator ⋮ Upper bounds for geodesic periods over rank one locally symmetric spaces ⋮ Effective equidistribution of twisted horocycle flows and horocycle maps ⋮ Integral moments of automorphic L-functions ⋮ Subconvex bounds for Hecke-Maass forms on compact arithmetic quotients of semisimple Lie groups ⋮ Lattice points counting and bounds on periods of Maass forms ⋮ Bounding hyperbolic and spherical coefficients of Maass forms

Cites Work

• Sparse equidistribution problems, period bounds and subconvexity
• Cusp forms and eigenfunctions of the Laplacian
• Eigenfunctions on symmetric spaces with distribution-valued boundary forms
• Analytic continuation of representations and estimates of automorphic forms
• Holomorphic extensions of representations. I: Automorphic functions
• Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. (On a new type of nonanalytic automorphic functions and the determination of Dirichlet series by functional equations)
• Positivity of quadratic base change $L$-functions
• Some applications of Gelfand pairs to number theory
• A new approach to the spectral theory of the fourth moment of the Riemann zeta-function
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Quantum unique ergodicity for \(\text{SL}_2 (\mathcal O)\backslash\mathbb{H}^3\) and estimates for \(L\)-functions
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