Kowalski–Michel–VanderKam mass equidistribution conjecture in the level aspect
Kowalski–Michel–VanderKam mass equidistribution conjecture in the level aspect
Let be a classical holomorphic newform of fixed weight and level , with mass on . Let be the canonical projection, and let denote the Poincaré measure on . Kowalski–Michel–VanderKam's mass equidistribution conjecture. If traverses a sequence of newforms of fixed weight and increasing level , then the pushforward equidistributes with respect to . This is the level-aspect analogue of the Rudnick–Sarnak quantum unique ergodicity conjecture, reversing the roles of weight and level; the supplied text does not state whether it has been resolved.
Sources & referencesView supporting material
Primary source
Paul D. Nelson, “Equidistribution of cusp forms in the level aspect”, arXiv:1011.1292 (2012).
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