圆与模曲面单位切丛乘积的联合等分布
Joint equidistribution on the product of the circle and the unit tangent bundle of the modular surface
摘要：
本文用谱方法证明了模曲面的圆与单位余切丛的乘积中的原有理点与原有理点沿扩展的均圈轨道的联合等分布。这一结果解释了Einsiedler、Luethi和Shah \cite [定理$1.1$ ]{ELS}最近工作中的误差界。错误是尖锐的最知名的进展对拉马努金猜想在有限的地方的模块化表面。
英文摘要：
We use spectral method to prove a joint equidistribution of primitive rational points and the same along expanding horocycle orbits in the products of the circle and the unit cotangent bundle of the modular surface. This result explicates the error bound in a recent work of Einsiedler, Luethi, and Shah \cite[Theorem $1.1$]{ELS}. The error is sharp upon the best known progress towards the Ramanujan conjecture at the finite places for the modular surface.
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