mjou_053_055_074.pdf 179 KB
Lee, Min Ho
Automorphic pseudodifferential operators are pseudodifferential operators that are invariant under an action of a discrete subgroup Γ of SL(2,ℝ), and they are closely linked to modular forms. In particular, there is a lifting map from modular forms to automorphic pseudodifferential operators, which can be interpreted as a lifting morphism of sheaves over the Riemann surface X associated to the given discrete subgroup Γ. One of the questions raised in a paper by Cohen, Manin, and Zagier is whether the difference in the images of a local section of a sheaf under such lifting morphisms corresponding to two projective structures on X can be expressed in terms of certain Schwarzian derivatives. The purpose of this paper is to provide a positive answer to this question for some special cases.
Automorphic pseudodifferential operators
Mathematical Journal of Okayama University
Department of Mathematics, Faculty of Science, Okayama University
Editorial Board of Mathematical Journal of Okayama University