A Siegel-Weil identity for \(G_2\) and poles of \(L\)-functions

DOI10.1006/jnth.1999.2480zbMath0958.11035OpenAlexW2084790502MaRDI QIDQ1568080

David Ginzburg, Di-Hua Jiang

Publication date: 11 April 2001

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1999.2480

zbMATH Keywords

Eisenstein seriesperiodscuspidal automorphic representation\(G_2\)polesRankin-Selberg integral\(F_4\)partial \(L\)-functionSiegel-Weil identity

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)

Related Items

Holomorphy of adjoint L-functions for \(\mathrm{GL}(n):n\le 4\), A Siegel-Weil formula for automorphic characters: Cubic variation of a theme of Snitz, Holomorphy of adjoint \(L\) functions for quasisplit \(A_2\)

Cites Work

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• Explicit constructions of automorphic \(L\)-functions
• Some remarks on nilpotent orbits
• Invariants d'un sous-groupe unipotent maximal d'un groupe semi-simple
• A Rankin-Selberg integral for the adjoint representation of \(GL_ 3\)
• The first term identities for Eisenstein series
• A regularized Siegel-Weil formula: The first term identity
• Fourier coefficients of Eisenstein series of the exceptional group of type \(G_2\)
• On spin \(L\)-functions for orthogonal groups
• On explicit lifts of cusp forms from \(\text{GL}_m\) to classical groups
• The adjoint L-function of GL(4)
• G2-periods and residual representations
• On the archimedean theory of Rankin-Selberg convolutions for ${\rm SO}_{2l+1}\times{\rm GL}_n$
• Degree 16 standard 𝐿-function of 𝐺𝑆𝑝(2)×𝐺𝑆𝑝(2)