An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups

2001/11/07 by D. Mayer, J. Neunhaeuserer
Mathematics · Physics and Astronomy · #math.NT #math-ph #math.DS #math.MP #msc:11F11 #msc:30F35 #msc:37C30

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published as Mathematical Physics Electronic Journal 7 (2001) 1-18 · 18 pages

arxiv created 2001/11/07 · arxiv updated 2009/11/30

Abstract

For the group PSL(2,Z) it is known that there is an isomorphism between polynomial eigenfunctions of the transfer operator for the geodesic flow and the Eichler cohomology in the theory of modular forms. In a recent paper by Chang and Mayer it is indicated that such an isomorphism exists as well for certain subgroups of PSL(2,Z). We prove this and provide some evidence by computer aided algebraic calculations that such an isomorphism exists for all principal congruence subgroups and all congruence subgroups of Hecke type.

Related

• Transfer operators for Γ₀(n) and the Hecke operators for the period functions for PSL(2,Z)
• Eigenfunctions of transfer operators and automorphic forms for Hecke triangle groups of infinite covolume
• Congruence properties of induced representations and their applications
• Conjugacy classes in PSL(2, K)
• Period functions for Hecke triangle groups, and the Selberg zeta function as a Fredholm determinant