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

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 determine…