Advances in Mathematics· 2026Q1
Quantum variance for holomorphic Hecke cusp forms on the vertical geodesic
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- 2026year
Short summary
We compute the quantum variance of holomorphic cusp forms on the vertical geodesic, relating it to an averaged shifted-convolution problem evaluated asymptotically.
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Key points
- The quantum variance of holomorphic cusp forms on the vertical geodesic is computed.
- The variance is linked to an averaged shifted-convolution problem.
- An asymptotic evaluation of the shifted-convolution problem is performed.
- An off-diagonal term is found to exactly match a diagonal term, similar to L-function moments.
AI-generated from the title and abstract; the full text is not read.
Abstract
We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth, compactly supported test functions. The variance is related to an averaged shifted-convolution problem that we evaluate asymptotically. We encounter an off-diagonal term that matches exactly with a certain diagonal term, a feature reminiscent of moments of L -functions.
The authors' abstract, as published at the source. Advances in Mathematics, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics