论文标题
扭曲模量的GL（2）
Twisting moduli for GL(2)
论文作者
论文摘要
我们证明了γ_0（n）上自动形式的各种匡威定理，每个形式的扭曲功能方程都比最后一个。我们表明，在n为18、20或24的情况下，全体形态模块化形式根本不需要扭曲 - 这些整数是4或9的最小倍数，而不是早期的Conrey -farmer工作。这种开发是找到针对γ_0（n）生成集的结果，因此每个发生器可以写成特殊矩阵的产物。至于实用分析的Maass形式（分别为奇数），我们证明了n = 1的类似陈述，... 12,16,18（分别n = 1，...，12,14,15,15,16,17,17,18,20,23,24）。
We prove various converse theorems for automorphic forms on Γ_0(N), each assuming fewer twisted functional equations than the last. We show that no twisting at all is needed for holomorphic modular forms in the case that N is 18, 20, or 24 - these integers are the smallest multiples of 4 or 9 not covered by earlier work of Conrey-Farmer. This development is a consequence of finding generating sets for Γ_0(N) such that each generator can be written as a product of special matrices. As for real-analytic Maass forms of even (resp. odd) weight we prove the analogous statement for N=1,...12,16,18 (resp. N=1,...,12,14,15,16,17,18,20,23,24).
