Degree 16 standard L-function of GSp(2) x GSp(2)

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American Mathematical Society , Providence, R.I
Automorphic functions., L-funct
Classifications The Physical Object Other titles Degree sixteen standard L-function of GSp(2) x GSp(2) Statement Dihua Jiang. Series Memoirs of the American Mathematical Society,, no. 588 LC Classifications QA3 .A57 no. 588, QA353.A9 .A57 no. 588 Pagination viii, 196 p. ; Open Library OL984158M ISBN 10 0821804766 LC Control Number 96021897

Get this from a library. Degree 16 standard L-function of GSp(2) x GSp(2). [Dihua Jiang] -- This memoir offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic Author: Dihua Jiang.

Genre/Form: Electronic books: Additional Physical Format: Print version: Jiang, Dihua. Degree 16 standard L-function of GSp(2) x GSp(2) / Material Type. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic.

American Mathematical Society Charles Street Providence, Rhode Island or AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Cited by: 2.

Degree 16 Standard L-Function of Gsp(2) X Gsp(2) (Memoirs of the American Mathematical Society) Oct 1, by Dihua Jiang Hardcover. $More Information Are you an author. Visit Author Central to change your photo, edit your. The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of Saito-Kurokawa type, in which case the. The L-function of degree 16 in Conjecture is related to the tensor product L-function in [Jia96]. In the example of Remark it coincides with the product of two shifted L-functions of. On L-functions for GSp(4) X GL(2) and their special values. Details Degree 16 standard L-function of GSp(2) x GSp(2) PDF On L-functions for GSp(4) X GL(2) and their special values. Furusawa, Masaaki Introduction The purpose of this paper is to present a new integral representation of a degree eight L-function for GSp(4) x GL(2). In principle our method always works when both forms correspond to holomorphic. Theorem we will obtain an integral representation for the degree-8 L-function L(s,πF ×τf) of GSp(4)× GL(2), where F is a vector-valued holomorphic Siegel modular cusp form of degree 2 (with respect to the full modular group) and fis an elliptic Maaß cusp form (of arbitrary level). Download Degree 16 standard L-function of GSp(2) x GSp(2) EPUB The integral representation isFile Size: KB. In our earlier paper, based on a paper by Bump and Ginzburg, we used an Eisenstein series on the double cover of $${\\text {GL}}(r)$$ GL (r) to obtain an integral representation of the twisted symmetric square L-function of $${\\text {GL}}(r)$$ GL (r). Using that, we showed that the (incomplete) twisted symmetric square L-function of$\${\\text Cited by: 6. We develop explicit formulas for Hecke operators of higher genus in terms of spherical coordinates. Applications are given to summation of various generating series with coefficients in local Hecke algebras and in a tensor product of such algebras.

In particular, we formulate and prove Rankin’s lemma in genus by: 1. To show that these are equal for each relevant Weyl groups element, the authors compute the Mellin transforms and match them in all cases.

The authors also describe the L-function heuristics which motivate this work, its possible generalizations, and an application of the relative trace formula to the study of L-packets. p-adic L-functions for GSp(4) x GL (2). Agarwal, Mahesh K.

In this thesis we construct a p-adic analog of a degree eight L-function L(s,Fxf) where F is an ordinary holomorphic degree 2 Siegel eigen cusp form of level a power of p and f is an ordinary eigen cusp form of level a power of by: 6.

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Williams Adobe Illustrator (3rd Ed), Tony Bove. seminar, TU Darmstadt (Germany), 4. Interactive open source e-book: Lectures on Linear Algebra, International Con-ference of Mathematical Sciences, Istanbul (Turkey), 5. On the standard L-function attached to Jacobi forms of higher index, Ecole d’Et e ZetasUniversit e Savoie Mont Blanc (France), File Size: KB.

Pitale et al. Notation Let G = GSp 4 be the group of symplectic similitudes of semisimple rank 2, deﬁned by GSp 4={g ∈ GL: t gJg= μ(g)J,μ(g) ∈ GL1}, where J = −12 0 Here, μ is called the similitude character. Let Sp 4 ={g ∈ GSp 4: μ(g) = 1}.TheSiegel parabolic subgroup P of GSp 4 consists of matrices whose lower left 2×2-block is zero.

Its unipotentradicalU. p (ν)×AI(χ)p) is the local p-factor of the GSp2 ×GL2 convolution L-function (degree 8) and L(s,πur p (ν),Ad) is the local p-factor of the adjoint L-function of GSp2 (degree 10). Let X0+ p denote the set of ν∈ Xp such that πur p (ν) is unitarizable.

Description Degree 16 standard L-function of GSp(2) x GSp(2) PDF

Note that X0+ p is a relatively compact subset of Xp and X0p ⊂ X0+ p. SinceAuthor: Masao Tsuzuki. L-function in the spirit of Deligne’s conjecture is proved.

1 Introduction Let Fbe a number eld and A its ring of adeles. Let ˇbe a cuspidal, automorphic representation of GSp 4 (A), and let ˝be a cuspidal, automorphic representation of GL 2(A). In his paper [7], Furusawa has obtained an integral representation for the GSp 4 GL.

Integral representation for L-functions for GSp 4 ×GL 2, II Ameya Pitale1, Ralf Schmidt2 Abstract. Based on Furusawa’s theory [7], we present an integral representation for the L-function L(s,π×τ), where π is a cuspidal automorphic representation on GSp 4 related to a holomorphic Siegel modular form, and where τ is an arbitrary cuspidal.

Abstract. We prove an algebraicity result for the central critical value of certain Rankin–Selberg L-functions for GL n × GL n− is a generalization and refinement of the results of Harder [], Kazhdan, Mazur, and Schmidt [], and Mahnkopf [].As an application of this result, we prove algebraicity results for certain critical values of the fifth and the seventh Cited by: Profit and Loss Statement (P&L): A profit and loss statement (P&L) is a financial statement that summarizes the revenues, costs and expenses incurred during a.

2 SPHERICAL BESSEL FUNCTIONS 4 unipotent radical U consists of all elements of the block form 1 X 1, where Xis symmetric. The standard Levi component M of P consists of all elements A utA 1 with u2GL1 and A2GL2.

Over the real numbers, we have the identity component G(R)+:= fg2GSp 4(R): (g) >0g. Let H2 be the Siegel upper half space of degree 2. Hence, an element Cited by: 2. Local and global Maass relations Ameya Pitale, Abhishek Saha and Ralf Schmidt Abstract.

We characterize the irreducible, admissible, spherical representations of GSp 4 (F) (where Fis a p-adic eld) that occur in certain CAP representations in terms of relations satis ed by their spherical vector in a special Bessel model.

As the partial standard L-function ζ S (Π ′, χ 0, s) of Π ′ has a pole at s = 1, by Theorem of and Section 5 of, Π ′ is a global theta lift from a representation of G O (V), where V is a 4-dimensional quadratic space over a corresponding discriminant algebra L; this is Author: Konstantinos Tsaltas, Frazer Jarvis.

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1 INTRODUCTION 3 with even kthere exists a cuspidal Siegel eigenform Fof weight ksuch that its spin L-function is given by L(s;F) = L(s;f) (s k+1) (s k+2)."In this case the Fourier coe cients of F are not readily available. At the very least, one would like to know that the Fourier coe cients of the modular form F constructed in the representation theoretic way satisfy the Maass relations.

I have been reading the book "Automorphic forms and Lie superalgebras". In SectionDefinition we have the definition of Category O for BKM Lie superalgebras (I have also checked the book. This volume uses a unified approach to representation theory and automorphic forms.

The invited papers, written by leading mathematicians, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their association with number theory and differential geometry. (The latter language has now been abandoned).

Gradually, IHES published two annual volumes totalling pages. Sincethe journal has had a circulation of printed copies. It is also available on line and on Les Publications mathématiques de l’IHES is an international journal publishing papers of highest scientific level.

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Visit Stack Exchange.L-function of GL(r) is holomorphic for Re(s) > 1. In this paper, we will determine the possible poles of this Eisenstein series more precisely and show that the (incomplete) twisted symmetric square L-function is entire except possible simple poles at s = 0 and s = 1.

1. Introduction Let ˇ˘= 0.Inthe international Iwasawa conference takes place in Bordeaux, from June 24 to It will be preceded by four mini-courses (of four hours each) on the topic.

Please note that registration is free, but required. The deadline is March 31st. For students applying for financial support, please write us before February 20th. Mini-courses (June 19 to 22): 1. Venkatesh's conjecture for.