Strong quantitative quantum ergodicity conjecture for Maass-Hecke cusp forms
Strong quantitative quantum ergodicity conjecture for Maass-Hecke cusp forms
Let be a Maass-Hecke cusp form with spectral parameter , Fourier coefficients , and let denote the Kronecker delta. For , write for its Sobolev norm. Strong QQUE conjecture. There exist and such that, for any ,
This is the strong rate-of-convergence form of arithmetic quantum unique ergodicity for the Fourier coefficients of Maass-Hecke cusp forms. The source presents it as the strong form of quantitative QUE, while the supplied text gives no resolution evidence, so its status remains open.
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Sources & referencesView supporting material
Primary source
Junehyuk Jung, “Quantitative quantum ergodicity and the nodal domains of Maass-Hecke cusp forms”, arXiv:1301.6211 (2016).
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