Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897102 | Journal of Number Theory | 2018 | 23 Pages |
Abstract
Let Sk!(Î1(N)) be the space of weakly holomorphic cusp forms of weight k on Î1(N) with an even integer k>2 and Mk!(Î1(N)) be the space of weakly holomorphic modular forms of weight k on Î1(N). Further, let z denote a complex variable and D:=12Ïiââz. In this paper, we construct a basis of the space Sk!(Î1(N))/Dkâ1(M2âk!(Î1(N))) consisting of Hecke eigenforms by using the Eichler-Shimura cohomology theory. Further, we study algebraicity of CM values of weakly holomorphic modular forms in the basis. This applies to an analogue of the Chowla-Selberg formula for a mock modular form whose shadow is the Ramanujan delta function.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Dohoon Choi, Subong Lim,