Qingfeng Sun, Qizhi Zhang
Published 2024-08-10Version 1
We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth compactly supported test functions. As an application we show that almost all holomorphic Hecke cusp forms, whose weights are in a short interval, satisfy QUE conjecture on the vertical geodesic.
Comments: 22 pages. arXiv admin note: substantial text overlap with arXiv:2111.04713 by other authors
The average of $L^4$-norms of holomorphic cusp forms
Large sums of Hecke eigenvalues of holomorphic cusp forms
The Dimension of the Space of Cusp Forms of Weight One
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