Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds

Fuente: arXiv
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Main Authors: Marshall, Simon, Narita, Hiroaki, Pitale, Ameya
Format: Preprint
Published: 2024
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author Marshall, Simon
Narita, Hiroaki
Pitale, Ameya
author_facet Marshall, Simon
Narita, Hiroaki
Pitale, Ameya
contents We give an explicit formula for the Petersson norms of theta lifts from Maass cusp forms of level one to cusp forms on orthogonal groups O(1,8n+1). Our formula explicitly determines archimedean local factors of the norms. As an application, we obtain the injectivity of the lifting of Maass forms and bounds on the sup-norm of cusp forms on these orthogonal groups in terms of their Laplace eigenvalues.
format Preprint
id arxiv_https___arxiv_org_abs_2404_04426
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds
Marshall, Simon
Narita, Hiroaki
Pitale, Ameya
Number Theory
We give an explicit formula for the Petersson norms of theta lifts from Maass cusp forms of level one to cusp forms on orthogonal groups O(1,8n+1). Our formula explicitly determines archimedean local factors of the norms. As an application, we obtain the injectivity of the lifting of Maass forms and bounds on the sup-norm of cusp forms on these orthogonal groups in terms of their Laplace eigenvalues.
title Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds
topic Number Theory
url https://arxiv.org/abs/2404.04426