Spectral aspect subconvex bounds for \(U_{n+1} \times U_n\)

DOI10.1007/s00222-023-01180-xzbMath1527.11039arXiv2012.02187OpenAlexW4323656658MaRDI QIDQ6040625

Paul D. Nelson

Publication date: 19 May 2023

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.02187

zbMATH Keywords

branching coefficientsubconvex boundunitary Gan-Gross-Prasad pair

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Geometric quantization (53D50) Zeta and (L)-functions: analytic theory (11M99)

Related Items

Group actions and harmonic analysis in number theory. Abstracts from the workshop held May 7--12, 2023

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fourier transform and the global Gan-Gross-Prasad conjecture for unitary groups
• The circle method and bounds for \(L\)-functions. IV: Subconvexity for twists of \(\mathrm{GL}(3)\) \(L\)-functions
• Sparse equidistribution problems, period bounds and subconvexity
• Subconvexity bounds for triple \(L\)-functions and representation theory
• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• Subconvexity for sup-norms of cusp forms on \(\mathrm{PGL}(n)\)
• Multiplicity one theorems: the Archimedean case
• The analysis of linear partial differential operators. III: Pseudo-differential operators
• Limit characters of reductive Lie groups
• Centralizers of irregular elements in reductive algebraic groups
• Tempered representations and orbits
• Kirillov's character formula for reductive Lie groups
• The subconvexity problem for Artin \(L\)-functions
• The subconvexity problem for \(\mathrm{GL}_2\)
• Bessel identities in the Waldspurger correspondence over the real numbers
• Subconvex bounds on \(\mathrm{GL}_3\) via degeneration to frequency zero
• \(L^ \infty\) norms of eigenfunctions of arithmetic surfaces
• Isolation of cuspidal spectrum, with application to the Gan-Gross-Prasad conjecture
• Distribution of Maass of holomorphic cusp forms
• The orbit method and analysis of automorphic forms
• The global Gan-Gross-Prasad conjecture for unitary groups: the endoscopic case
• On the subconvexity problem for \(\mathrm{GL}(3)\times\mathrm{GL}(2)\) \(L\)-functions
• On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture
• Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\)
• On sums of \(\mathrm{SL}(3,\mathbb{Z})\) Kloosterman sums
• On quantum unique ergodicity for locally symmetric spaces
• The Spectral Kuznetsov Formula on $SL(3)$
• The Refined Gross–Prasad Conjecture for Unitary Groups
• Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures
• SPHERICAL FUNCTIONS FORGL_nOVER LOCAL FIELDS, AND SUMMATION OF HECKE SERIES
• On the subconvexity problem for L-functions on GL(3)
• The Sup-Norm Problem for PGL(4)
• Fourth moments of grossencharakteren zeta functions
• Nonstandard Set Theory
• The spectral growth of automorphic L-functions.
• Internal set theory: A new approach to nonstandard analysis
• Merits and demerits of the orbit method
• Periods and harmonic analysis on spherical varieties
• COMPARISON OF LOCAL RELATIVE CHARACTERS AND THE ICHINO–IKEDA CONJECTURE FOR UNITARY GROUPS
• Subconvexity for $L$-functions of non-spherical cusp forms on ${\rm GL}(3)$
• The circle method and bounds for 𝐿-functions—III: 𝑡-aspect subconvexity for 𝐺𝐿(3) 𝐿-functions
• Lie Group Representations on Polynomial Rings
• Automorphic period and the central value of Rankin-Selberg L-function