Corpus ID: 237634987

Pullback formula for vector valued Siegel modular forms and its applications

@inproceedings{Kozima2021PullbackFF,
  title={Pullback formula for vector valued Siegel modular forms and its applications},
  author={Noritomo Kozima},
  year={2021}
}
where (C,D) runs over coprime symmetric pairs of degree n. The Eisenstein series converges for k+2Re(s) > n+1. As is well known, E k (Z, s) has meromorphic continuation to the whole s-plane and satisfies a functional equation. On the other hand, let f be a Siegel cuspform of weight k with respect to Sp(q,Z) (size 2q). Suppose f is an eigenform, i.e., a non-zero common eigenfunction of the Hecke algebra. Then taking Petersson inner 
Harder's conjecture I
Let f be a primitive form with respect to SL2(Z). Then, we propose a conjecture on the congruence between the Klingen-Eisenstein lift of the Duke-Imamoglu-Ikeda lift of f and a certain lift of aExpand

References

SHOWING 1-10 OF 21 REFERENCES
Garrett's pullback formula for vector valued Siegel modular forms
Abstract Let E k n be the Siegel Eisenstein series of degree n and weight k. Garrett showed a formula of E k p + q on H p × H q , where H n is the Siegel upper half space of degree n. This formulaExpand
Standard L-functions attached to alternating tensor valued Siegel modular forms
Let (ρ ρ) be an irreducible rational representation of ( C) on a finitedimensional complex vector space ρ such that the signature of ρ is (λ1 λ2 . . . λ ) ∈ Z with λ1 ≥ λ2 ≥ · · · ≥ λ ≥ 0. Let be aExpand
On standard L-functions attached to altⁿ-¹(Cⁿ)-valued Siegel modular forms
In [23], we studied some properties of standard L-functions attached to sym'( Iθ-valued Siegel modular forms of weight det* (x) sym*. More precisely, let det* (x) sym be an irreducible rationalExpand
Eisenstein series on the symplectic group
Analytic continuation is proved for certain Eisenstein series on the symplectic group which are associated with nonparabolic forms. In the case of the full modular group an explicit functionalExpand
The classical groups
In this chapter we describe the six families of so-called ‘classical’ simple groups. These are the linear, unitary and symplectic groups, and the three families of orthogonal groups. All may beExpand
On the Functional Equations Satisfied by Eisenstein Series
The assumptions.- Cusp forms.- Eisenstein series.- Miscellaneous lemmas.- Some functional equations.- The main theorem.
Die analytische Fortsetzung der Eisensteinreihe zur Siegelschen Modulgruppe.
Auf halbeinfachen Liegruppen sind die Eisensteinreihen sehr allgemein definiert. Die analytische Fortsetzung dieser Eisensteinreihen beweist Langlands [7] mittels Spektralzerlegung. Obwohl KalininExpand
Über Funktionalgleichungen automorpher L-Funktionen zur Siegelschen Modulgruppe.
Andrianov ist es gelungen, diese L-Funktion durch eine Dirichletreihe auszudrücken, in die nur die Fourierkoeffizienten von/eingehen [2], [3]. Daraus kann man — wie im wesentlichen in [4] ausgeführtExpand
Eisenstein series for Siegel modular groups
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