The Riemann Zeta function arises as the constant term of the Eisenstein series \(G_{2 k}\), and we noted that rationality of \(\zeta(1-2 k)\) then followed from properties of \(G_{2 k}\).
Eisenstein series
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Riemann Zeta
Related to Eisenstein series:
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AWS 2022: Automorphic Forms Beyond \(\operatorname{GL}_2\)
Rationality of L functions: try to reduce to a question about Eisenstein series. Strategy: