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• W2971344959 abstract "We improve upon the local bound in the depth aspect for sup-norms of newforms on $D^times$ where $D$ is an indefinite quaternion division algebra over $mathbb{Q}$. Our sup-norm bound implies a depth-aspect subconvexity bound for $L(1/2, f times theta_chi)$, where $f$ is a (varying) newform on $D^times$ of level $p^n$, and $theta_chi$ is an (essentially fixed) automorphic form on $mathrm{GL}_2$ obtained as the theta lift of a Hecke character $chi$ on a quadratic field. For the proof, we augment the amplification method with a novel filtration argument and a recent counting result proved by the second-named author to reduce to showing strong quantitative decay of matrix coefficients of local newvectors along compact subsets, which we establish via $p$-adic stationary phase analysis. Furthermore, we prove a general upper bound in the level aspect for sup-norms of automorphic forms belonging to emph{any} family whose associated matrix coefficients have such a decay property." @default.
• W2971344959 created "2019-09-05" @default.
• W2971344959 creator A5007562898 @default.
• W2971344959 creator A5028120984 @default.
• W2971344959 date "2019-05-15" @default.
• W2971344959 modified "2023-09-25" @default.
• W2971344959 title "Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity" @default.
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• W2971344959 doi "https://doi.org/10.48550/arxiv.1905.06295" @default.
• W2971344959 hasPublicationYear "2019" @default.
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