The special values of the standard L-functions for \GSp_2n\n \× \GL₁

2021/02/05 by Shuji Horinaga, Horinaga, Shuji, Ameya Pitale +5
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2102.03100

openalex publication_date 2021/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the expected algebraicity property for the critical values of\ncharacter twists of the standard L-function associated to vector-valued\nholomorphic Siegel cusp forms of archimedean type (k₁, k₂, \…, k_n),\nwhere k_n \≥ n+1 and all k_i are of the same parity. For the proof, we\nuse an explicit integral representation to reduce to arithmetic properties of\ndifferential operators on vector-valued nearly holomorphic Siegel cusp forms.\nWe establish these properties via a representation-theoretic approach.\n

Citations

• The doubling Archimedean zeta integrals for p-adic interpolation

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