On Eisenstein series

DOI10.1215/S0012-7094-83-05019-6zbMath0519.10019OpenAlexW2009994141MaRDI QIDQ1054767

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1215/s0012-7094-83-05019-6

zbMATH Keywords

unitary group analytic continuation Euler product congruence subgroups Siegel series confluent hypergeometric functions on tube domains Eisenstein series on symplectic group Hecke Grenzprozess

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Other groups and their modular and automorphic forms (several variables) (11F55)

Related Items

On the critical values of \(L\)-functions of \(GL(2)\) and \(GL(2)\times GL(2)\) ⋮ On Hermitian Eisenstein series ⋮ Vector valued theta series and Waldspurger's theorem ⋮ Motives over totally real fields and \(p\)-adic \(L\)-functions ⋮ On the representations generated by Eisenstein series of weight \(\frac{n + 3}{2}\) ⋮ Note on Siegel-Eisenstein series of low weight ⋮ Nearly holomorphic functions on Hermitian symmetric spaces ⋮ On Hilbert modular forms of half-integral weight ⋮ Eisenstein series and zeta functions on symplectic groups ⋮ Zeta functions and Eisenstein series on metaplectic groups ⋮ Explicit formulae of Siegel Eisenstein series ⋮ L-functions attached to Jacobi forms of degree n. II: Functional equation ⋮ On the analytic continuation of certain Poincaré series of elliptic modular groups ⋮ On mod \(p\) singular modular forms ⋮ Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields ⋮ Determination of holomorphic modular forms by primitive Fourier coefficients ⋮ On the critical values of certain Dirichlet series and the periods of automorphic forms ⋮ Explicit formulas for local factors: Addenda and errata ⋮ On integrality of Eisenstein liftings ⋮ On Siegel series for Hermitian forms. II ⋮ Derivative of the standard 𝑝-adic 𝐿-function associated with a Siegel form ⋮ Note on Siegel-Eisenstein series ⋮ Nearly holomorphic Eisenstein liftings ⋮ Convergence of zeta functions on symplectic and metaplectic groups ⋮ On the Fourier coefficients of nonholomorphic Hilbert modular forms of half-integral weight ⋮ Yoshida lifts and Selmer groups ⋮ Fourier coefficients of the Siegel Eisenstein series of degree 2 with odd prime level, corresponding to the middle cusp ⋮ ON THE GRADED RING OF SIEGEL MODULAR FORMS OF DEGREE TWO WITH RESPECT TO A NON-SPLIT SYMPLECTIC GROUP ⋮ \(p\)-adic Siegel-Eisenstein series of degree two ⋮ Eigenvalues of certain differential operators related to automorphic forms ⋮ Correspondence among Eisenstein series of weight 2 ⋮ Using Katsurada’s determination of the Eisenstein series to compute Siegel eigenforms ⋮ Special cycles on unitary Shimura varieties. I: Unramified local theory ⋮ On \(p\)-adic Hermitian Eisenstein series and \(p\)-adic Siegel cusp forms ⋮ Correction to: ``Poles and residues of standard \(L\)-functions attached to Siegel modular forms ⋮ On the mod \(p\) kernel of the theta operator and Eisenstein series ⋮ Nearly holomorphic automorphic forms on \(\text{SL}_2\) ⋮ On some \(p\)-adic properties of Siegel-Eisenstein series. ⋮ An explicit formula for Siegel series ⋮ Exact critical values of the symmetric fourth \(L\) function and vector valued Siegel modular forms ⋮ Theta dichotomy for unitary groups ⋮ An integral representation of standard automorphic \(L\) functions for unitary groups ⋮ A short proof of the Kitaoka-Feit induction lemma for Siegel series ⋮ On the Bloch-Kato conjecture for elliptic modular forms of square-free level ⋮ The critical values of certain Dirichlet series attached to Hilbert modular forms ⋮ An exact mass formula for orthogonal groups. ⋮ On mod \(p\) properties of Siegel modular forms ⋮ Fourier coefficients of certain Eisenstein series ⋮ On the arithmetic of Siegel-Hilbert cusp forms: Petersson inner products and Fourier coefficients ⋮ On the Siegel Eisenstein series of degree two for low weights ⋮ Zeta functions and Eisenstein series on classical groups ⋮ Eisenstein Congruences for SO(4, 3), SO(4, 4), Spinor, and Triple ProductL-values ⋮ Triple products of Coleman's families ⋮ Phantom holomorphic projections arising from Sturm's formula ⋮ Eisenstein series on quaternion half-space of degree 2 ⋮ Siegel Eisenstein series of degree \(n\) and \(\lambda\)-adic Eisenstein series ⋮ Families of Siegel modular forms, \(L\)-functions and modularity lifting conjectures ⋮ Some Siegel modular standard \(L\)-values, and Shafarevich-Tate groups ⋮ On the Siegel-Eisenstein measure and its applications ⋮ Arithmeticity of holomorphic cuspforms on Hermitian symmetric domains ⋮ Eisenstein series on quaternion half-space of degree \(n\) ⋮ Confluent hypergeometric functions on an exceptional domain ⋮ A remark on the normalization of the standard zeta values for Siegel modular forms ⋮ On the standard \(L\)-function for \(\mathrm{GSp}_{2n}\times\mathrm{GL}_1\) and algebraicity of symmetric fourth \(L\)-values for \(\mathrm{GL}_2\) ⋮ Special values and mixed weight triple products (with an appendix by Don Blasius) ⋮ Appendix to Orloff. Critical values of certain tensor product L- functions ⋮ On Siegel series for Hermitian forms ⋮ On \(p\)-adic L-functions of \(GL(2)\times GL(2)\) over totally real fields ⋮ Eisenstein series of weight \(n+1\) on Siegel's modular group of \(n\)th degree ⋮ Critical values of \(L\)-functions on \(\text{GSp}_2 \times \text{GL}_2\) ⋮ Note on \(p\)-adic Hermitian Eisenstein series ⋮ On the analytic properties of the standard \(L\)-function attached to Siegel-Jacobi modular forms ⋮ A note on the Siegel-Eisenstein series of weight 2 on \(Sp_ 2(\mathbb{Z})\) ⋮ Constructions of nearly holomorphic Siegel modular forms of degree two ⋮ Eisenstein series on tube domains ⋮ On Eisenstein series for the Hermitian modular groups and the Jacobi groups ⋮ On 𝑝-adic Hermitian Eisenstein series ⋮ Congruence Primes of the Kim–Ramakrishnan–Shahidi Lift ⋮ On a theorem of Waldspurger and on Eisenstein series of Klingen type ⋮ Poles and residues of standard L-functions attached to Siegel modular forms ⋮ On \(p\)-adic \(L\)-functions of \(GL(2) \times{} GL(2)\) over totally real fields ⋮ Unnamed Item ⋮ On differential operators attached to certain representations of classical groups ⋮ Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series ⋮ Hyperbolic equidistribution problems on Siegel 3-folds and Hilbert modular varieties ⋮ Unnamed Item ⋮ \(p\)-adic measures attached to Siegel modular forms ⋮ Differential operators and the singular values of Eisenstein series ⋮ Congruences for Fourier coefficients of lifted Siegel modular forms. I: Eisenstein lifts ⋮ On the Fourier coefficients of Hilbert modular forms of half-integral weight ⋮ On Eisenstein series of half-integral weight ⋮ Eisenstein series for Siegel modular groups ⋮ Class numbers, Jacobi forms and Siegel-Eisenstein series of weight 2 on \(\text{Sp}_ 2(\mathbb{Z})\) ⋮ Euler products and Fourier coefficients of automorphic forms on symplectic groups

Cites Work