On central critical values of the degree four 𝐿-functions for GSp(4): the fundamental lemma

DOI10.1090/memo/0782zbMath1026.11050OpenAlexW2018924422WikidataQ125057027 ScholiaQ125057027MaRDI QIDQ4416607

Masaaki Furusawa, Joseph A. Shalika

Publication date: 3 August 2003

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0782

zbMATH Keywords

relative trace formulafundamental lemmaKloosterman integral

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Gauss and Kloosterman sums; generalizations (11L05) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (12)

Local root numbers, Bessel models, and a conjecture of Guo and Jacquet ⋮ On central critical values of the degree four \(L\)-functions for \(\mathrm{GSp}(4)\): a simple trace formula ⋮ Fourier expansion of Arakawa lifting. I: An explicit formula and examples of non-vanishing lifts ⋮ On inversion of the Bessel and Gelfand transforms ⋮ Fourier expansion of Arakawa lifting II: Relation with central L-values ⋮ On tensor product \(L\)-functions for quaternion unitary groups and \(\mathrm{GL}(2)\) over totally real number fields: mixed weight cases ⋮ Formulas for central values of twisted spin $L$-functions attached to paramodular forms ⋮ Refined global Gross-Prasad conjecture on special Bessel periods and Böcherer's conjecture ⋮ Transfer of Siegel cusp forms of degree 2 ⋮ A relation between multiplicity one and Böcherer's conjecture ⋮ On central critical values of the degree four $L$-functions for $\mathrm {GSp}(4)$: The fundamental lemma. III ⋮ Local factors of nongeneric supercuspidal representations of \(\mathrm{GSp}_4\)

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