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{{Infobox scientist
| name              = Hervé Jacquet
| image            = <!--(filename only)-->
| image_size        =
| caption          =
| birth_date        = {{birth year and age|df=yes|1939}}
| birth_place      = France
| death_date        =
| death_place      =
| nationality      = French
| fields            = Mathematics
| workplaces        = [[Columbia University]]
| alma_mater        = [[École Normale Supérieure]]
| doctoral_advisor  = [[Roger Godement]]
| doctoral_students = [[Dinakar Ramakrishnan]]<br>[[Yangbo Ye]]
| known_for        =
| awards            =
}}
'''Hervé Jacquet''' is a [[French American]] mathematician, working in [[automorphic forms]]. He is considered one of the founders of the theory of [[Automorphic forms#Automorphic representations|automorphic representations]] and their associated [[L-functions]], and his results play a central role in modern [[number theory]].
 
==Career==
Jacquet entered the [[École Normale Supérieure]] in 1959 and obtained his doctorat d'état under the direction of [[Roger Godement]] in 1967. He held academic positions at the [[Centre National de la Recherche Scientifique]] (1963–1969), the [[Institute for Advanced Study]] in [[Princeton, New Jersey|Princeton]] (1967–1969), the [[University of Maryland at College Park]] (1969–1970), the [[CUNY Graduate Center|Graduate Center]] of the [[City University of New York]] (1970–1974), and became a Professor at [[Columbia University]] in 1974, becoming Professor Emeritus in 2007.
 
==Mathematical work==
The book by Hervé Jacquet and [[Robert Langlands]] on <math>GL(2)</math><ref>H. Jacquet and R. P. Langlands. Automorphic forms on GL(2), Lecture Notes in Mathematics, Vol.114, Springer-Verlag, Berlin (1970).</ref> was an eclipsing event in the history of number theory. It presented a [[representation theory]] of automorphic forms and their associated L−functions for the [[general linear group]] <math>GL(2)</math>, establishing among other things the [[Jacquet-Langlands correspondence]] which explains very precisely how automorphic forms for <math>GL(2)</math> relate to those for [[quaternion algebras]]. Equally important was the book by Roger Godement and Hervé Jacquet,<ref>H. Jacquet and J. A. Shalika. A non-vanishing theorem for zeta functions of GLn. Invent. Math., 38(1):1–16, 1976/77.</ref> which defined, for the first time, the standard L-functions attached to automorphic representations of <math>GL(n)</math>, now called Godement-Jacquet L-functions, and proved their basic, oft-used analytic properties. The papers with Shalika<ref>H. Jacquet and J. A. Shalika. On Euler products and the classification of automorphic forms, I, Amer. J. Math. 103(3): 499–558 (1981).</ref><ref>H. Jacquet and J. A. Shalika. On Euler products and the classification of automorphic forms, II, Amer. J. Math. 103(4): 777–815 (1981).</ref> and the papers with [[Ilya Piatetski-Shapiro|Piatetski-Shapiro]] and Shalika<ref>H. Jacquet, I. I. Piatetski-Shapiro and J. A. Shalika. Automorphic forms on GL(3). I. Ann. of Math. (2), 109(1):169–212, 1979.</ref><ref>H. Jacquet, I. I. Piatetski-Shapiro and J. A. Shalika.
Automorphic forms on GL(3). II. Ann. of Math. (2), 109(2):213–258, 1979.</ref><ref>H. Jacquet, I. I. Piatetski-Shapiro and J. A. Shalika. Rankin-Selberg convolutions. Amer. J. Math., 105(2):367–464, 1983.</ref> pertain to L-functions of pairs, called the Rankin-Selberg L-functions, attached to representations of <math>GL(n)</math> and <math>GL(m)</math>, and the so-called converse theorem, which are crucial to our understanding of automorphic forms. A basic ingredient of this effort was an elaboration of properties of [[Whittaker models]] and [[Whittaker functions|functions]], which Jacquet had made contributions to since his thesis. The papers with Shalika also established the uniqueness of isobaric decompositions of automorphic forms on <math>GL(n)</math>, thus providing evidence for certain conjectures of Langlands. In the mid-eighties, Jacquet forayed into a new territory in the field and created<ref>H. Jacquet. Sur un résultat de Waldspurger. Ann. Sci. École Norm. Sup. (4), 19(2):185–229, 1986.</ref><ref>H. Jacquet. Représentations distinguées pour le groupe orthogonal. C. R. Acad. Sci. Paris Sér. I Math., 312(13):957–961, 1991.</ref><ref>H. Jacquet and K. F. Lai. A relative trace formula, [[Compositio Mathematica]], 54(2), 243–310 (1985).</ref> the [[relative trace formula]] in representation theory, an important tool in modern number theory, which vastly generalizes the [[Kuznetsov trace formula|Kuznetsov]] and [[Petersson trace formula|Petersson formulae]] from the classical setup. While the usual [[Selberg trace formula]], as well as its generalizations due to Arthur, consists in developing an expression for the integral of the kernel over the diagonal, the relative version integrates the kernel over other appropriate subgroups.
 
==Awards and honors==
He was elected corresponding member of the [[Académie des Sciences]] in 1980. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-26.</ref> He was elected to the [[American Academy of Arts and Sciences]] in 2013.<ref>[http://amacad.org/news/classlist2013.pdf Newly elected members], [[American Academy of Arts and Sciences]], April 2013, retrieved 2013-04-24.</ref>
 
==See also==
 
*[[Jacquet functor]]
*[[Jacquet–Langlands correspondence]]
*[[Jacquet module]]
 
==References==
{{Reflist}}
 
==External links==
*[http://www.math.columbia.edu/fac-bios/Jacquet/faculty.html Columbia University Faculty Bio]
* {{MathGenealogy|id=11897}}
 
{{Authority control|VIAF=12833974}}
 
{{Persondata        <!-- Metadata: see [[Wikipedia:Persondata]] -->
| NAME              =Jacquet, Herve
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = french mathematician
| DATE OF BIRTH    = 1939
| PLACE OF BIRTH    = France
| DATE OF DEATH    =
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Jacquet, Herve}}
[[Category:1939 births]]
[[Category:Living people]]
[[Category:French mathematicians]]
[[Category:20th-century mathematicians]]
[[Category:Number theorists]]
[[Category:Columbia University faculty]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Fellows of the American Mathematical Society]]
[[Category:Fellows of the American Academy of Arts and Sciences]]

Latest revision as of 04:36, 25 December 2014

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