2022/07/12 by Bo‐Hae Im, Wonwoong Lee, Im, Bo-Hae +1
Mathematics · #11F30 (Secondary) #11F37 (Primary) 11F06 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2207.05325
openalex publication_date 2022/07/12 · openalex created_date 2022/07/15 · openalex updated_date 2026/07/28
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).