论文标题
季节模块化形式和中央$ l $值的零
Zeroes of quaternionic modular forms and central $L$-values
论文作者
论文摘要
Quaternionic模块化形式的值与扭曲的中央$ l $值有关，并通过waldspurger定理。特别是，某些扭曲的$ l $ - 价值对于没有零的表格必须不逐渐呈现。在这里，我们在理论上和计算上研究了琐碎重量的确定的Quaternionic模块化形式的零。局部标志条件迫使某些形式具有微不足道的零，但是我们猜想几乎所有形式都没有非平凡的零。特别是，几乎所有具有适当本地标志的表格都不应为零。我们表明了这些猜想是从平均纪念轨道数量的猜想中遵循的，并将申请（非）消失的$ l $价值提供。
Values of quaternionic modular forms are related to twisted central $L$-values via periods and a theorem of Waldspurger. In particular, certain twisted $L$-values must be non-vanishing for forms with no zeroes. Here we study, theoretically and computationally, zeroes of definite quaternionic modular forms of trivial weight. Local sign conditions force certain forms to have trivial zeroes, but we conjecture that almost all forms have no nontrivial zeroes. In particular, almost all forms with appropriate local signs should have no zeroes. We show these conjectures follow from a conjecture on the average number of Galois orbits, and give applications to (non)vanishing of $L$-values.
