Journal of the Ramanujan Mathematical Society

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A Theta Function Identity and the Eisenstein Series on Γ0(5)


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1 East China Normal University, Department of Mathematics, Shanghai 200241, China
     

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We prove an identity connecting a theta function and a sum of Eisenstein series by using the complex variable theory of elliptic functions, which contains as a special case a famous identity of Ramanujan connected with partitions modulus 5. This identity allows us to develop a theory for the Eisenstein series on the congruence subgroup Γ0(5). Combining this identity with two identities in Ramanujan’s lost notebook, a curious Eisenstein series identity related to the Rogers-Ramanujan continued fraction is derived.
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  • A Theta Function Identity and the Eisenstein Series on Γ0(5)

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Authors

Zhi-Guo Liu
East China Normal University, Department of Mathematics, Shanghai 200241, China

Abstract


We prove an identity connecting a theta function and a sum of Eisenstein series by using the complex variable theory of elliptic functions, which contains as a special case a famous identity of Ramanujan connected with partitions modulus 5. This identity allows us to develop a theory for the Eisenstein series on the congruence subgroup Γ0(5). Combining this identity with two identities in Ramanujan’s lost notebook, a curious Eisenstein series identity related to the Rogers-Ramanujan continued fraction is derived.