Spectral aspect subconvex bounds for Un+1× Un

Paul D. Nelson

doi:10.1007/s00222-023-01180-x

Spectral aspect subconvex bounds for U_n₊₁× U_n

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

2 Citationer (Scopus)

Abstract

Let (π, σ) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan–Gross–Prasad pair (U_n₊₁, U_n) over a number field, with U_n anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex bound L(π×σ,1/2)≪C(π×σ)1/4-δholds for any fixed δ<18n5+28n4+42n3+36n2+14n.Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.

Originalsprog	Engelsk
Tidsskrift	Inventiones Mathematicae
Vol/bind	232
Nummer	3
Sider (fra-til)	1273-1438
Antal sider	166
ISSN	0020-9910
DOI	https://doi.org/10.1007/s00222-023-01180-x
Status	Udgivet - jun. 2023

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Citationsformater

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title = "Spectral aspect subconvex bounds for Un+1× Un",

abstract = "Let (π, σ) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan–Gross–Prasad pair (Un+1, Un) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex bound L(π×σ,1/2)≪C(π×σ)1/4-δholds for any fixed δ<18n5+28n4+42n3+36n2+14n.Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.",

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N2 - Let (π, σ) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan–Gross–Prasad pair (Un+1, Un) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex bound L(π×σ,1/2)≪C(π×σ)1/4-δholds for any fixed δ<18n5+28n4+42n3+36n2+14n.Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.

AB - Let (π, σ) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan–Gross–Prasad pair (Un+1, Un) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex bound L(π×σ,1/2)≪C(π×σ)1/4-δholds for any fixed δ<18n5+28n4+42n3+36n2+14n.Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.

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