Random Eigenfunctions on Flat Tori: Universality for the Number of Intersections

Abstract

We show that several statistics of the number of intersections between random eigenfunctions of general eigenvalues with a given smooth curve in flat tori are universal under various families of randomness.2010 Mathematics Subject Classification. 15A52,11B25, 60C05, 60G50. Key words and phrases. arithmetic random waves, universality phenomenon, arithmetic progressions. M. C.

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