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arXiv · 2404.04426

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

Simon Marshall·Hiroaki Narita·Ameya Pitale
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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.

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Simon Marshall, Hiroaki Narita, Ameya Pitale. 2024-04-05. Petersson norms of Borcherds theta lifts to O(1, 8n+1) with applications to injectivity and sup-norm bounds. https://arxiv.org/abs/2404.04426

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