 Fourier expansion of a normalized Eisenstein series

ID: fourier-expansion-of-a-normalized-eisenstein-series

Codex  0 Created 2026-09-28 Updated 2026-10-05

For even

k \geq 4

, the normalized level-one Eisenstein series has expansion

E_{k} (τ) = 1 + \frac{2}{ζ ( 1 - k )} \sum_{n \geq 1} σ_{k - 1} (n) q^{n} = 1 - \frac{2 k}{B _{k}} \sum_{n \geq 1} σ_{k - 1} (n) q^{n} .

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