Periods and liftings: From \(G_2\) to \(C_3\)

DOI10.1007/BF02784119zbMath1005.11023MaRDI QIDQ5939274

Di-Hua Jiang, David Ginzburg

Publication date: 18 June 2002

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

zbMATH Keywords

\(L\)-functionsminimal representationperiodstheta lift

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) 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) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55) Modular correspondences, etc. (11F32)

Related Items (15)

A spectral identity between symmetric spaces ⋮ CAP representations of \(G_{2}\) and the spin \(L\)-function of \(\mathrm{PGSp}_6\) ⋮ On automorphic descent from \(GL_7\) to \(G_2\) ⋮ Periods of automorphic forms, poles of \(L\)-functions and functorial lifting ⋮ A local Langlands parameterization for generic supercuspidal representations of $p$-adic $G_2$ ⋮ Howe duality and dichotomy for exceptional theta correspondences ⋮ On certain Rankin-Selberg Integrals on GE₆ ⋮ Subgroups of \(\mathrm{Spin}(7)\) or \(\mathrm{SO}(7)\) with each element conjugate to some element of \(\mathrm{G}_2\) and applications to automorphic forms ⋮ Dichotomy for generic supercuspidal representations ofG₂ ⋮ Endoscopic lifting in classical groups and poles of tensor \(L\)-functions ⋮ Poles of the Standard -function of and the Rallis–Schiffmann Lift ⋮ Branching rules obtained from explicit correspondences of automorphic representations ⋮ An exceptional Siegel–Weil formula and poles of the Spin L-function of ⋮ A new tower of Rankin-Selberg integrals ⋮ On Spin L-functions for GSO 10

Cites Work

• On the Ramanujan conjecture and finiteness of poles for certain \(L\)-functions
• A trace formula for reductive groups. I: Terms associated to classes in G(Q)
• Test vectors for linear forms
• On the standard \(L\)-function for \(G_ 2\)
• Rankin-Selberg integrals in two complex variables
• A tower of theta correspondences for \(G_ 2\)
• On the discrete spectrum of \((G_2, PGSp_6)\)
• On the automorphic theta representation for simply laced groups
• The spin \(L\)-function on the symplectic group GSp(6)
• On the theory of Jacobi forms and Fourier-Jacobi coefficients of Eisenstein series
• G2-periods and residual representations
• Nonvanishing of the central critical value of the third symmetric power L-functions
• On standard L-functions for E6 and E7.
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