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

Hiro-aki Narita, Ameya Pitale

Type: Preprint

Publication Date: 2024-04-05

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2404.04426

Abstract

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.

Locations

arXiv (Cornell University) - View - PDF

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