Algebraicity of Spin L-functions for GSp₆

2024/08/06 by Ellen Eischen, Giovanni Rosso, Eischen, Ellen +3
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Advanced Algebra and Geometry #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.2408.03442

Abstract

We prove algebraicity of critical values of certain Spin L-functions. More precisely, our results concern L(s, π⊗ χ, Spin) for cuspidal automorphic representations π associated to a holomorphic Siegel eigenform on GSp₆, real Dirichlet characters χ, and critical points s to the right of the center of symmetry. We use the strategy of relating the L-values to properties of Eisenstein series, and a significant portion of the paper concerns the Fourier coefficients of these Eisenstein series. Unlike in prior algebraicity results following this strategy, our Eisenstein series are on a group G that has no known moduli problem, and the L-functions are related to the Eisenstein series through a non-unique model.

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