Period integrals and Rankin-Selberg \(L\)-functions on \(\mathrm{GL}(n)\)

DOI10.1007/s00039-012-0166-7zbMath1317.11049arXiv1106.2296OpenAlexW2064157265MaRDI QIDQ1938487

Valentin Blomer

Publication date: 4 February 2013

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2296

zbMATH Keywords

momentsEisenstein seriesRankin-Selberg \(L\)-functionsautomorphic forms on \(\mathrm{GL}(n)\)

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) 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)

Related Items (7)

The second moment of Rankin–Selberg L-functions ⋮ Subconvexity for half integral weight \(L\)-functions ⋮ Zeros of Rankin–Selberg L-functions in families ⋮ Nonvanishing of Rankin-Selberg \(L\)-functions for Hilbert modular forms ⋮ Bounds for twisted symmetric square L-functions via half-integral weight periods ⋮ Non-vanishing of Rankin-Selberg convolutions for Hilbert modular forms ⋮ Applications of analytic newvectors for \(\operatorname{GL}(N)\)

Uses Software

• GL(n)pack

Cites Work

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• Sparse equidistribution problems, period bounds and subconvexity
• Subconvexity bounds for triple \(L\)-functions and representation theory
• The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points. II
• Trilinear forms and the central values of triple product \(L\)-functions
• Archimedean \(L\)-factors on \(\text{GL}(n)\times\text{GL}(n)\) and generalized Barnes integrals
• The subconvexity problem for \(\mathrm{GL}_2\)
• Rankin-Selberg \(L\)-functions in the level aspect.
• Spectral asymptotics for arithmetic quotients of \(\text{SL}(n,{\mathbb R})/\text{SO}(n)\)
• A new bound K2/3+  for Rankin-Selberg L-functions for Hecke congruence subgroups
• Bessel Series Expansions of the Epstein Zeta Function and the Functional Equation
• Upper Bounds on L-Functions at the Edge of the Critical Strip
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• Level Aspect Subconvexity For Rankin-Selberg $L$-functions
• Estimates for Rankin-Selberg \(L\)-functions and quantum unique ergodicity

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