Local Integral Transforms and Global Spectral Decomposition

We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic $L$ L -functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.

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Bibliographic Details
Published in	Geometric and functional analysis
Main Authors	Blomer, Valentin, Jana, Subhajit, Nelson, Paul D.
Format	Journal Article
Language	English
Published	10.07.2025
Online Access	Get full text

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Summary:	We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic $L$ L -functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.
ISSN:	1016-443X 1420-8970
DOI:	10.1007/s00039-025-00714-0