Please use this identifier to cite or link to this item: http://hdl.handle.net/1783.1/7420

Operads and hecke operators on modular forms

Authors Wang, Chongli
Issue Date 2011
Summary Let Mk(Γ) be the collection of modular forms over C of weight k with respect to a congruence subgroup Γ, it is well-known double cosets ΓgΓact on it as linear maps. Those operators are known as Hecke operators. In this paper, we first show that similar double cosets ΓngΔΓ give multi-linear maps Mk1(Γ) x ⋅ ⋅ ⋅ x Mkn(Γ) → Mk1+⋅⋅⋅+kn(Γ), and we show these operators form an algebraic structure called operad . Then we define a Galois action on this operad which is compatible with the Galois action on modular forms. By taking the Galois orbit, we find a suboperad which acts on the integral modular forms.
Note Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2011
Subjects
Language English
Format Thesis
Access
Files in this item:
File Description Size Format
th_redirect.html 343 B HTML