Sobolev norms of local zeta integrals

Lingzhi Gu; Feng Su

doi:10.1093/qmath/haaf011

Sobolev norms of local zeta integrals

Lingzhi Gu, Feng Su

Research output: Contribution to journal › Article › peer-review

Abstract

We study the continuity of archimedean zeta integrals, as well as the lower bound of their operator norms, with respect to a natural family of Sobolev norms arising from the functional calculus of harmonic oscillator. The relevant notion and results will be generalized to archimedean Rankin–Selberg integrals of the tempered principal series representations of general linear groups.

Original language	English
Pages (from-to)	469-501
Number of pages	33
Journal	Quarterly Journal of Mathematics
Volume	76
Issue number	2
DOIs	https://doi.org/10.1093/qmath/haaf011
State	Published - 1 Jun 2025
Externally published	Yes

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© The Author(s) 2025. Published by Oxford University Press. All rights reserved.

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Sobolev norms of local zeta integrals

Abstract

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