Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772542 | Journal of Number Theory | 2017 | 28 Pages |
Abstract
Let Î be a Fuchsian group of the first kind. The Eichler-Shimura isomorphism states that the space Sk(Î) is isomorphic to the first (parabolic) cohomology group associated to the Î-module Rkâ1 with an appropriate Î-action. Manin reformulated the Eichler-Shimura isomorphism for the case Î=SL2(Z) in terms of periods of cusp forms. In this paper we extend Manin's reformulation to the case Î=Î0+(p) with pâ{2,3}. The Manin relations describe relations between periods of cusp forms by using Hecke operators and continued fractions. We also extend the Manin relations and homogeneity theorem to cusp forms on Î0+(2) without using continued fractions.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
SoYoung Choi, Chang Heon Kim,