Memoirs of the American Mathematical Society 1993; 100 pp; softcover Volume: 105 ISBN10: 0821825682 ISBN13: 9780821825686 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/105/500
 This work studies the local theory for certain RankinSelberg 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 halfplane 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  Introduction and preliminaries
 The integrals to be studied
 Estimates for Whittaker functions on \(G_\ell\) (nonarchimedean case)
 Estimates for Whittaker functions on \(G_\ell\) (archimedean case)
 Convergence of the integrals (nonarchimedean case)
 Convergence of the integrals (archimedean case)
 \(A(W,\xi _{\tau ,s})\) can be made constant (nonarchimedean case)
 An analog in the archimedean case
 Uniqueness theorems
 Application of the intertwining operator
 Definition of local factors
 Multiplicativity of the \(\gamma\)factor (case \(\ell < n\), first variable)
 The unramified computation
