Poles of Siegel Eisenstein Series on <i>U</i>(<i>n, n</i>)

Tan, Victor

doi:10.4153/cjm-1999-010-4

Cited by 35 publications

(27 citation statements)

References 7 publications

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“…On the other hand, ifˆ.s/ is the Siegel-Weil section associated to a factorizable ', we have a factorization [17,51] Here, for Re.s/ > n, the Whittaker function (discussed in more detail in Section 10 below) is given by…”

Section: The Siegel Formulamentioning

confidence: 99%

Special cycles on unitary Shimura varieties II: Global theory

Kudla

Rapoport

2013

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

145

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We introduce moduli spaces of abelian varieties which are arithmetic models of Shimura varieties attached to unitary groups of signature .n 1; 1/. We define arithmetic cycles on these models and study their intersection behavior. In particular, in the non-degenerate case, we prove a relation between their intersection numbers and Fourier coefficients of the derivative at s D 0 of a certain incoherent Eisenstein series for the group U.n; n/. This is done by relating the arithmetic cycles to their formal counterpart from part I [33] via nonarchimedean uniformization, and by relating the Fourier coefficients to the derivatives of representation densities of hermitian forms. The result then follows from the main theorem of part I and a counting argument.

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Section: The Siegel Formulamentioning

confidence: 99%

Special cycles on unitary Shimura varieties II: Global theory

Kudla

Rapoport

2013

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

145

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“…For a standard section f (s) of I (s, χ), Tan [27] proved that the poles of E(g, f (s) ) in Re(s) ≥ 0 are at most simple and occur at the points…”

Section: Siegel Eisenstein Seriesmentioning

confidence: 99%

A regularized Siegel-Weil formula for unitary groups

Ichino

2004

Mathematische Zeitschrift

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“…ii) Assume we are in Case A or B. Then, up to scalars, W # is the unique K G 2 ∞ -finite element of I W (s, χ, χ 0 , τ ) with the properties (85) and (86).…”

Section: Proof As a Subspace Ofmentioning

confidence: 99%

Untitled

2014

Memoirs of the AMS

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Let π be the automorphic representation of GSp 4 (A) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and τ be an arbitrary cuspidal, automorphic representation of GL 2 (A). Using Furusawa's integral representation for GSp 4 × GL 2 combined with a pullback formula involving the unitary group GU(3, 3), we prove that the L-functions L(s, π × τ) are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations π have a functorial lifting to a cuspidal representation of GL 4 (A). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of π to a cuspidal representation of GL 5 (A). As an application, we obtain analytic properties of various L-functions related to full level Siegel cusp forms. We also obtain special value results for GSp 4 × GL 1 and GSp 4 × GL 2 .

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Poles of Siegel Eisenstein Series on U(n, n)

Abstract: Abstract. Let U (n, n) be the rank n quasi-split unitary group over a number field. We show that the normalized Siegel Eisenstein series of U (n, n) has at most simple poles at the integers or half integers in certain strip of the complex plane.

Cited by 35 publications

References 7 publications

Special cycles on unitary Shimura varieties II: Global theory

Special cycles on unitary Shimura varieties II: Global theory

A regularized Siegel-Weil formula for unitary groups

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