论文标题
某些Fuchsian群体和班级数的非形态艾森斯坦系列
Non-holomorphic Eisenstein series for certain Fuchsian groups and class numbers
论文作者
论文摘要
我们研究以$ r（n）$表示的某些类型的Fuchsian群体，它们与Fricke群体或低级别的算术Hecke三角形群相吻合。我们为Prime $ p $ $ r（p）$找到了所有椭圆点和尖，并证明了$ r（p）$的椭圆点与假想的二次级别组之间有一对一的对应关系。我们还为$ r（n）$的非形态Eisenstein系列的傅立叶扩展的明确公式并研究了它们的分析性能。这些非形态的Eisenstein系列以及尖式形式为$ r（n）$的多结式马斯形式的空间提供了基础。
We study certain types of Fuchsian groups of the first kind denoted by $R(N)$, which coincide with the Fricke groups or the arithmetic Hecke triangle groups of low levels. We find all elliptic points and cusps of $R(p)$ for a prime $p$, and prove that there is a one-to-one correspondence between the set of equivalence classes of elliptic points of $R(p)$ and the imaginary quadratic class group. We also find the explicit formula of the Fourier expansion of the non-holomorphic Eisenstein series for $R(N)$ and study their analytic properties. These non-holomorphic Eisenstein series together with cusp forms provide a basis for the space of polyharmonic Maass forms for $R(N)$.
