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Title: Operads and hecke operators on modular forms
Authors: Wang, Chongli
Issue Date: 2011
Abstract: 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.
Description: Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2011
ix, 44 p. : ill. ; 30 cm
HKUST Call Number: Thesis MATH 2011 WangC
Appears in Collections:MATH Master Theses

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