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- W2767929871 abstract "We show an asymptotic formula for the L^2 norm of the Eisenstein series restricted to a segment of a geodesic connecting infinity and an arbitrary real. For generic geodesics of this form, the asymptotic formula shows that the Eisenstein series satisfies restricted QUE. On the other hand, for rational geodesics, the Eisenstein series does not satisfy restricted quantum ergodicity. As an application, we show that the zero set of the Eisenstein series intersects every such geodesic segment, provided the spectral parameter is large. We also make analogous conjectures for the Maass cusp forms. In particular, we predict that cusp forms do not satisfy restricted quantum ergodicity for rational geodesics." @default.
- W2767929871 created "2017-11-17" @default.
- W2767929871 creator A5047737822 @default.
- W2767929871 date "2018-12-01" @default.
- W2767929871 modified "2023-10-17" @default.
- W2767929871 title "Equidistribution of Eisenstein series on geodesic segments" @default.
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- W2767929871 doi "https://doi.org/10.1016/j.aim.2018.10.030" @default.
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