Differential operators and the singular values of Eisenstein series

DOI10.1215/S0012-7094-84-05115-9zbMath0546.10025OpenAlexW1559449288MaRDI QIDQ798355

Goro Shimura

Publication date: 1984

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-84-05115-9

zbMATH Keywords

symplectic groupunitary groupdifferential operatorsalgebraicity theoremcritical value of Dirichlet seriesEisenstein series at CM-point

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) Complex multiplication and moduli of abelian varieties (11G15) Automorphic functions in symmetric domains (32N15)

Related Items

On Hermitian Eisenstein series ⋮ Differential operators, holomorphic projection, and singular forms ⋮ Nearly holomorphic functions on Hermitian symmetric spaces ⋮ Eisenstein series and zeta functions on symplectic groups ⋮ On the critical values of certain Dirichlet series and the periods of automorphic forms ⋮ Eigenvalues of certain differential operators related to automorphic forms ⋮ \(p\)-adic differential operators on automorphic forms on unitary groups ⋮ Differential operators, pullbacks, and families of automorphic forms on unitary groups ⋮ Special values and mixed weight triple products (with an appendix by Don Blasius) ⋮ Appendix to Orloff. Critical values of certain tensor product L- functions ⋮ Critical values of \(L\)-functions on \(\text{GSp}_2 \times \text{GL}_2\) ⋮ On differential operators attached to certain representations of classical groups ⋮ WEIGHT CHANGING OPERATORS FOR AUTOMORPHIC FORMS ON GRASSMANNIANS AND DIFFERENTIAL PROPERTIES OF CERTAIN THETA LIFTS ⋮ \(p\)-adic measures attached to Siegel modular forms ⋮ Invariant differential operators on Hermitian symmetric spaces and their eigenvalues

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