THESIS
2011
ix, 44 p. : ill. ; 30 cm
Abstract
Let M
k(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 Γ
ngΔΓ give multi-linear maps
k1 kn k1+⋅⋅⋅+kn...[
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Let M
k(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 Γ
ngΔΓ give multi-linear maps
M
k1(Γ) x ⋅ ⋅ ⋅ x M
kn(Γ) → M
k1+⋅⋅⋅+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.
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