These pages are not updated anymore. For the current production of this journal, please refer to http://www.jstor.org/journals/0003486x.html.
Annals of Mathematics, II. Series Vol. 150, No. 2, pp. 645662 (1999) 

Symmetric cube $L$functions for $\text{GL}_2$ are entireHenry H. Kim and Freydoon ShahidiReview from Zentralblatt MATH: The authors prove the holomorphy of the symmetric cube $L$functions for non monomial cusp forms. Their method is representationtheoretic and relies on the works of {\it G. Muic} [Duke Math. J. 90, 465493 (1997; Zbl 0883.11020)]. Since the reviewer is not an expert, I will quote from the authors' introduction: ` To be more precise, let $F$ be a number field whose ring of adeles is $\Bbb A = \Bbb A_F$. Let $\pi = \otimes_v \pi_v$ be a cuspidal (unitary) representation of $GL_2(\Bbb A)$. Let $S$ be a finite set of places of $F$ such that for $V \not\in S$, $\pi_v$ is unramified. For each $v\not \in S$, let $$ t_v = \left\{ \pmatrix \alpha_v & 0 A weakened form of the main result of this paper is: If $\pi$ is not monomial, then the partial symmetric cube $L$function $L_S(s,\pi,r_3)$ is entire. Reviewed by Kevin L.James Keywords: holomorphy; symmetric cube $L$function; nonmonomial cusp forms Classification (MSC2000): 11F66 11F70 Full text of the article:
Electronic fulltext finalized on: 8 Sep 2001. This page was last modified: 21 Jan 2002.
© 2001 Johns Hopkins University Press
