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Rankin-Selberg Convolutions for $\mathrm{SO}_{2\ell +1}\times \mathrm{GL}_n$ : Local Theory
 
Front Cover for Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory
Available Formats:
Electronic ISBN: 978-1-4704-0077-4
Product Code: MEMO/105/500.E
List Price: $36.00
MAA Member Price: $32.40
AMS Member Price: $21.60
Front Cover for Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory
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  • Front Cover for Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory
  • Back Cover for Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory
Rankin-Selberg Convolutions for $\mathrm{SO}_{2\ell +1}\times \mathrm{GL}_n$ : Local Theory
Available Formats:
Electronic ISBN:  978-1-4704-0077-4
Product Code:  MEMO/105/500.E
List Price: $36.00
MAA Member Price: $32.40
AMS Member Price: $21.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1051993; 100 pp
    MSC: Primary 11; 22; 26; 32;

    This work studies the local theory for certain Rankin-Selberg convolutions for the standard \(L\)-function of degree \(2\ell n\) of generic representations of \(\mathrm{ SO}_{2\ell +1}(F)\times \mathrm{GL}_n(F)\) over a local field \(F\). The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and \(L\)-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor (\(\ell < n\), first variable). A special case of this result yields the unramified computation and involves a new idea not presented before. This presentation, which contains detailed proofs of the results, is useful to specialists in automorphic forms, representation theory, and \(L\)-functions, as well as to those in other areas who wish to apply these results or use them in other cases.

    Readership

    Mathematicians working in automorphic forms, representation theory of reductive groups over local fields, \(L\)-functions and \(\epsilon\) functions.

  • Table of Contents
     
     
    • Chapters
    • 0. Introduction and preliminaries
    • 1. The integrals to be studied
    • 2. Estimates for Whittaker functions on $G_l$ (nonarchimedean case)
    • 3. Estimates for Whittaker functions on $G_l$ (archimedean case)
    • 4. Convergence of the integrals (nonarchimedean case)
    • 5. Convergence of the integrals (archimedean case)
    • 6. $A(W, \xi _{r,s})$ can be made constant (nonarchimedean case)
    • 7. An analog in the archimedean case
    • 8. Uniqueness theorems
    • 9. Application of the intertwining operator
    • 10. Definition of local factors
    • 11. Multiplicativity of the $\gamma $-factor (case $l < n$, first variable)
    • 12. The unramified computation
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Volume: 1051993; 100 pp
MSC: Primary 11; 22; 26; 32;

This work studies the local theory for certain Rankin-Selberg convolutions for the standard \(L\)-function of degree \(2\ell n\) of generic representations of \(\mathrm{ SO}_{2\ell +1}(F)\times \mathrm{GL}_n(F)\) over a local field \(F\). The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and \(L\)-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor (\(\ell < n\), first variable). A special case of this result yields the unramified computation and involves a new idea not presented before. This presentation, which contains detailed proofs of the results, is useful to specialists in automorphic forms, representation theory, and \(L\)-functions, as well as to those in other areas who wish to apply these results or use them in other cases.

Readership

Mathematicians working in automorphic forms, representation theory of reductive groups over local fields, \(L\)-functions and \(\epsilon\) functions.

  • Chapters
  • 0. Introduction and preliminaries
  • 1. The integrals to be studied
  • 2. Estimates for Whittaker functions on $G_l$ (nonarchimedean case)
  • 3. Estimates for Whittaker functions on $G_l$ (archimedean case)
  • 4. Convergence of the integrals (nonarchimedean case)
  • 5. Convergence of the integrals (archimedean case)
  • 6. $A(W, \xi _{r,s})$ can be made constant (nonarchimedean case)
  • 7. An analog in the archimedean case
  • 8. Uniqueness theorems
  • 9. Application of the intertwining operator
  • 10. Definition of local factors
  • 11. Multiplicativity of the $\gamma $-factor (case $l < n$, first variable)
  • 12. The unramified computation
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