Eisenstein Cohomology and Critical Values of Certain L-Functions: The Case G₂

2025/01/07 by Farid HosseiniJafari, HosseiniJafari, Farid
Mathematics · #11F66 #11F67 #11F70 #11F75 #20G05 #22E5 #22E50 #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.2501.03546

openalex publication_date 2025/01/07 · openalex created_date 2025/01/09 · openalex updated_date 2026/07/28

Abstract

We establish results on the rationality of ratios of successive critical values of Langlands-Shahidi L-functions, as they appear in the constant term of the Eisenstein series associated with the exceptional group of type G₂ over a totally imaginary number field. Furthermore, we prove the rationality of the critical values for each L-function in the products, such as the symmetric cube L-functions. Our method generalizes the Harder-Raghuram method to cases where multiple L-functions appear in the constant term and involve an exceptional group. Finally, our results on the automorphic version of Deligne's conjecture align with its motivic counterpart, as demonstrated in the recent work of Deligne and Raghuram.

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