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Transfer of Siegel Cusp Forms of Degree 2
 
Ameya Pitale :  University of Oklahoma, Norman, Oklahoma
Abhishek Saha :  University of Bristol, Bristol, United Kingdom
Ralf Schmidt :  University of Oklahoma, Norman, Oklahoma
Transfer of Siegel Cusp Forms of Degree 2
eBook ISBN:  978-1-4704-1893-9
Product Code:  MEMO/232/1090.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Add to cart
Transfer of Siegel Cusp Forms of Degree 2
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Transfer of Siegel Cusp Forms of Degree 2
Ameya Pitale :  University of Oklahoma, Norman, Oklahoma
Abhishek Saha :  University of Bristol, Bristol, United Kingdom
Ralf Schmidt :  University of Oklahoma, Norman, Oklahoma
eBook ISBN:  978-1-4704-1893-9
Product Code:  MEMO/232/1090.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 232; 2014; 107 pp
    MSC: Primary 11

    Let \(\pi\) be the automorphic representation of \(\textrm{GSp}_4(\mathbb{A})\) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and \(\tau\) be an arbitrary cuspidal, automorphic representation of \(\textrm{GL}_2(\mathbb{A})\). Using Furusawa's integral representation for \(\textrm{GSp}_4\times\textrm{GL}_2\) combined with a pullback formula involving the unitary group \(\textrm{GU}(3,3)\), the authors prove that the \(L\)-functions \(L(s,\pi\times\tau)\) are “nice”.

    The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations \(\pi\) have a functorial lifting to a cuspidal representation of \(\textrm{GL}_4(\mathbb{A})\). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of \(\pi\) to a cuspidal representation of \(\textrm{GL}_5(\mathbb{A})\).

    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 \(\textrm{GSp}_4\times\textrm{GL}_1\) and \(\textrm{GSp}_4\times\textrm{GL}_2\).
  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Notation
    • 1. Distinguished vectors in local representations
    • 2. Global $L$-functions for $\textup {GSp}_4\times \textup {GL}_2$
    • 3. The pullback formula
    • 4. Holomorphy of global $L$-functions for $\textup {GSp}_4 \times \textup {GL}_2$
    • 5. Applications
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 232; 2014; 107 pp
MSC: Primary 11

Let \(\pi\) be the automorphic representation of \(\textrm{GSp}_4(\mathbb{A})\) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and \(\tau\) be an arbitrary cuspidal, automorphic representation of \(\textrm{GL}_2(\mathbb{A})\). Using Furusawa's integral representation for \(\textrm{GSp}_4\times\textrm{GL}_2\) combined with a pullback formula involving the unitary group \(\textrm{GU}(3,3)\), the authors prove that the \(L\)-functions \(L(s,\pi\times\tau)\) are “nice”.

The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations \(\pi\) have a functorial lifting to a cuspidal representation of \(\textrm{GL}_4(\mathbb{A})\). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of \(\pi\) to a cuspidal representation of \(\textrm{GL}_5(\mathbb{A})\).

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 \(\textrm{GSp}_4\times\textrm{GL}_1\) and \(\textrm{GSp}_4\times\textrm{GL}_2\).
  • Chapters
  • Introduction
  • Notation
  • 1. Distinguished vectors in local representations
  • 2. Global $L$-functions for $\textup {GSp}_4\times \textup {GL}_2$
  • 3. The pullback formula
  • 4. Holomorphy of global $L$-functions for $\textup {GSp}_4 \times \textup {GL}_2$
  • 5. Applications
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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