论文标题
二次Hecke总和和质量分布
Quadratic Hecke sums and mass equidistribution
论文作者
论文摘要
我们考虑了量子型hecke特征形式在紧凑型算术双曲表面上的量子独特的构型猜想的类似物。我们表明，这种猜想是从二次进程中总结的Hecke特征值的非平凡界限遵循的。我们的还原为Luo-sarnak为非紧凑型模块表面的情况建立的标准的紧凑型案例提供了类似物。新颖性是，此类标准的已知证据取决于傅立叶扩张，这在紧凑型情况下不可用。无条件地，我们建立了Holowinsky-Soundararajan定理的扭曲变体，该变体涉及限制通过基础变化引起的归一化Hilbert模块化形式。
We consider the analogue of the quantum unique ergodicity conjecture for holomorphic Hecke eigenforms on compact arithmetic hyperbolic surfaces. We show that this conjecture follows from nontrivial bounds for Hecke eigenvalues summed over quadratic progressions. Our reduction provides an analogue for the compact case of a criterion established by Luo--Sarnak for the case of the non-compact modular surface. The novelty is that known proofs of such criteria have depended crucially upon Fourier expansions, which are not available in the compact case. Unconditionally, we establish a twisted variant of the Holowinsky--Soundararajan theorem involving restrictions of normalized Hilbert modular forms arising via base change.
