Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis


Image from Google Jackets

Transfer of Siegel cusp forms of degree 2 / Ameya Pitale, Abhishek Saha and Ralf Schmidt.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 232, no 1090.Publication details: Providence : American Mathematical Society, c2014.Description: v, 107 p. ; 25 cmISBN:
  • 9780821898567 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
Introduction-- Notation-- 1. Distinguished vectors in local representations-- 2. Global L-functions for GSp4 X GL2-- 3. The pullback formula-- 4. Holomorphy of global L-functions for GSp4 X GL2-- 5. Applications-- Bibliography.
Summary: Let p be the automorphic representation of GSp4 ( A ) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and t be an arbitrary cuspidal, automorphic representation of GL? ( A ). Using Furusawa's integral representation for GSp? X GL? combined with a pullback formula involving the unitary group GU (3,3), the authors prove that the L-functions L(s, p X t are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations p have a functorial lifting to a cuspidal representation of GL? ( A ). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of p to a cuspidal representation of GL5 ( A ). As an application, the authors obtain analytic properties of various L-functions related to full level Siegel cusp forms. They also obtain special value results for GSp? X GL? and GSp4 X GL?.
Tags from this library: No tags from this library for this title. Log in to add tags.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 135881
Total holds: 0

"November 2014, volume 232, number 1090 (second of 6 numbers)"

Includes bibliographical references (pages 103-107).

Introduction--
Notation--
1. Distinguished vectors in local representations--
2. Global L-functions for GSp4 X GL2--
3. The pullback formula--
4. Holomorphy of global L-functions for GSp4 X GL2--
5. Applications--
Bibliography.

Let p be the automorphic representation of GSp4 ( A ) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and t be an arbitrary cuspidal, automorphic representation of GL? ( A ). Using Furusawa's integral representation for GSp? X GL? combined with a pullback formula involving the unitary group GU (3,3), the authors prove that the L-functions L(s, p X t are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations p have a functorial lifting to a cuspidal representation of GL? ( A ). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of p to a cuspidal representation of GL5 ( A ). As an application, the authors obtain analytic properties of various L-functions related to full level Siegel cusp forms. They also obtain special value results for GSp? X GL? and GSp4 X GL?.

There are no comments on this title.

to post a comment.
Library, Documentation and Information Science Division, Indian Statistical Institute, 203 B T Road, Kolkata 700108, INDIA
Phone no. 91-33-2575 2100, Fax no. 91-33-2578 1412, ksatpathy@isical.ac.in