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arXiv · 2404.10692

Local integral transforms and global spectral decomposition

Valentin Blomer·Subhajit Jana·Paul D. Nelson
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Abstract

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

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Valentin Blomer, Subhajit Jana, Paul D. Nelson. 2024-04-16. Local integral transforms and global spectral decomposition. https://doi.org/10.1007/s00039-025-00714-0

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