In Memoriam: Joseph A. Shalika 1941-2010
Freydoon Shahidi
American Journal of Mathematics, Volume 132, Number 6, December
2010, pp. iii-iv (Article)
Published by The Johns Hopkins University Press

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IN MEMORIAM:JOSEPH A. SHALIKA
1941–2010

Photo courtesy of JHU Mathematics

I started my graduate studies at the Johns Hopkins University in 1971, thesame year that Joe Shalika moved back to his alma mater. His sharp intelligenceand talent, together with his cheerful and kind personality very quickly attracted
me to work with him as his first student, a warm friendship that lasted throughout
our lives.
Shalika’s contributions to representation theory and automorphic forms arenumerous. His thesis under F. I. Mautner is still considered as a pioneering
work in p–adic group representations. The joint work with Paul Sally on explicit
Plancherel formulas for SL(2) which followed seems to have found recent interestin Langlands’ new ideas on functoriality.

His first global result appeared in a joint work with S. Tanaka, constructing
automorphic forms on SL(2) by means of theta distributions as suggested by Weil.
Following Harish–Chandra, he proved what is now called the “Shalika germ
expansion” for semisimple orbital integrals of semisimple groups, central objects
in Arthur’s trace formula whose unramified matchings, the so called “Fundamental Lemma”, was recently proved by Bao Châu Ngô.
A large portion of Shalika’s career was devoted to the theory of L–functions
for GL(n), all of it joint with Hervé Jacquet and a few by both of them and thelate Ilya Piatetski–Shapiro. This rich theory of zeta functions, which occupies
an important chapter in number theory, has played a central role in the theoryof automorphic forms and the Langlands program, culminating in two major
papers in the American Journal of Mathematics that allowed them to classify
automorphic representations of GL(n) over number fields. Central to this theoryis his important joint work with Bill Casselman, which generalized Shintani’swork and gave a formula for unramified Whittaker functions on any reductive
group, a result of significance in my own work.
Shalika’s career continued to the end of his life through his work with hislater students, M. Furusawa and R. Takloo–Bighash, working mainly on arithmetic
aspects of the theory, and in part with Y. Tschinkel. Joe served as chair of theDepartment of Mathematics at Hopkins from 1979 to 1982. He was also anAssociate Editor of the American Journal of Mathematics from 1984 to 1993.
Joe’s 60th birthday was celebrated with a conference organized by Dinakar
Ramakrishnan, Steve Zelditch, and me at Hopkins in May of 2002. He was very
happy and delighted to see many of his old friends who came for the occasion.
A volume was later published in honor of his birthday by the JHU Press.
Joe never lost his love for mathematics. Our dinner conversation during mylast visit in April of 2010 was mainly occupied with mathematical discussions
and his latest work with Furusawa, at the end of which I promised to send him
a number of papers of interest, which I did.
Joe rarely traveled, but those who met him were taken by his unassuming,kind, and generous personality. After his retirement in 2009, many of us lost
contact with him and if it wasn’t for an accidental encounter with a former
student of Igusa, Leon Strauss, we would not have had the fine memories ofphone conversations and visits that took place in the last year of his life, memories
which I now cherish every moment of.
Joe Shalika passed away on September 18, 2010. He was 69. He will bemissed by all of us.
Freydoon Shahidi, October 2010