Holomorphy of Rankin triple \(L\)-functions; special values and root numbers for symmetric cube \(L\)-functions

DOI10.1007/BF02834847zbMath1005.11026OpenAlexW2464746313MaRDI QIDQ5930679

Freydoon Shahidi, Henry H. Kim

Publication date: 25 February 2003

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02834847

zbMATH Keywords

cusp forms on GL(2)Deligne's conjectureholomorphy of Rankin triple \(L\)-functionslocal Langlands correspondencespecial values of symmetric cube \(L\)-functions

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (5)

On algebraicity of special values of symmetric 4-th and 6-th power \(L\)-functions for \(\operatorname{GL}(2)\) ⋮ On the mean-square of the error term related to \(\sum_{n\leq x} \lambda^2 (n^j)\) ⋮ Values of symmetric cube $L$-functions and Fourier coefficients of Siegel Eisenstein series of degree-3 ⋮ Langlands-Shahidi method and poles of automorphic \(L\)-functions. II. ⋮ Boundedness of automorphic 𝐿–functions in vertical strips

Cites Work

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• Decomposition of Eisenstein series: Rankin triple products
• Special values and mixed weight triple products (with an appendix by Don Blasius)
• Appendix to Orloff. Critical values of certain tensor product L- functions
• The central critical value of a triple product \(L\)-function
• On the Ramanujan conjecture and finiteness of poles for certain \(L\)-functions
• Local coefficients as Artin factors for real groups
• The Langlands conjecture for \(\mathrm{GL}_2\) of a local field
• Some results on the unramified principal series of \(p\)-adic groups
• On the functional equations satisfied by Eisenstein series
• On the periods of modular forms
• Spectral decomposition and Eisenstein series
• On the coefficients of cusp forms
• The residual spectrum of the group of type \(G_ 2\)
• The unitary dual of \(p\)-adic \(G_2\)
• The holomorphy and nonvanishing of normalized local intertwining operators
• Langlands-Shahidi method and poles of automorphic \(L\)-functions. II.
• Modularity of the Rankin-Selberg \(L\)-series, and multiplicity one for \(\mathrm{SL}(2)\)
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• Symmetric cube \(L\)-functions for \(\text{GL}_2\) are entire
• A simple proof of Langlands conjectures for \(\text{GL}_n\) on a \(p\)-adic field
• Rankin-Selberg Convolutions
• The Residual Spectrum ofG₂
• Le spectre résiduel de ${\rm GL}(n)$
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• L-Indistinguishability For SL (2)
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$
• On irreducibility of standard modules for generic representations
• Langlands-Shahidi Method and Poles of Automorphic L-Functions: Application to Exterior Square L-Functions
• Local Rankin-Selberg convolutions for 𝐺𝐿_{𝑛}: Explicit conductor formula
• Special Values of Triple Product L-Functions

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