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Abstract We study “partition Eisenstein series”, extensions of the Eisenstein series G 2 k (τ) G₂₊ (), defined by λ = (1 m 1, 2 m 2, …, k m k) ⊢ k ↦ G λ (τ): = G 2 (τ) m 1 G 4 (τ) m 2 ⋯ G 2 k (τ) m k. = (1^m₁, 2^m₂, , k^m₊) k G_ () %: =G₂ () ^m₁G₄ () ^m₂ G₂₊ () ^m₊. For functions ϕ: 𝒫 ↦ ℂ: P on partitions, the weight 2 k 2k </jat
Amdeberhan et al. (Mon,) studied this question.
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