240:. The 1990 Wolf Prize to Piatetski–Shapiro cites this work with Rallis as one of Piatetski–Shapiro's main achievements. Whereas it had previously been assumed that all the L-functions constructed by the Rankin–Selberg integral method were a subset of those constructed by the Langlands–Shahidi method, the 1992 paper by Rallis with Piatetski-Shapiro and Schiffmann on the Rankin–Selberg integrals for the group G_2 showed this was not the case and opened the way for determining many new examples of L-functions represented by Rankin–Selberg integrals.
28:
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255:) to classical groups". Their automorphic descent method constructs an explicit inverse map to the (standard) Langlands functorial lift and has had major applications to the analysis of functoriality. Also, using the "Rallis tower property" from his 1984 paper on the Howe duality conjecture, Rallis with Ginzburg and Soudry studied global exceptional correspondences and found new examples of functorial lifts.
235:
was the start of his work on what is now known as "The Rallis Inner
Product Formula" which relates the inner product of a pair of theta functions to a special value or residue of a Langlands L-function. This cornerstone of what Wee Teck Gan et al. term the Rallis program on the theta correspondence
236:
has found wide applications. Rallis then adapted the classical idea of doubling a quadratic space to create the "Piatetski–Shapiro and Rallis
Doubling Method" for constructing integral representations of L-functions, and thus they obtained the first general result on L-functions for all
262:
in Kyoto. In 2003, the conference "Automorphic
Representations, L-Functions and Applications: Progress and Prospects" was held in honor of Rallis's 60th birthday and according to the conference proceedings, "reflects the depth and breadth of Rallis's influence". In January, 2015, the
231:: the regularized Siegel–Weil formula and the first term identity. These results have prompted other mathematicians to extend Siegel–Weil to other cases. Rallis' 1984 paper giving proofs of certain examples of the
269:
published a special issue in honor of Steve Rallis's contributions to mathematics. Rallis has the distinction of having his biography included in the MacTutor
History of Mathematics archive.
666:
W.T. Gan, Y. Qiu, and S. Takeda (2014)"The
Regularized Siegel–Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula," Inventiones Math. 198, 739–831
594:
W.T. Gan, Y. Qiu, and S. Takeda (2014)"The
Regularized Siegel–Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula," Inventiones Math. 198, 739–831
563:
W.T. Gan, Y. Qiu, and S. Takeda (2014)"The
Regularized Siegel–Weil Formula (The Second Term Identity) and the Rallis Inner Product Formula," Inventiones Math. 198, 739–831
675:
S. Rallis "Poles of standard L functions," Proceedings of the
International Congress of Mathematicians (Kyoto, 1990), Vol. I, II (1991), 833–845, Math. Soc. Japan, Tokyo.
686:
Automorphic
Representations, L-Functions and Applications: Progress and Prospects: Proceedings of a Conference honoring Steve Rallis on the occasion of his 60th birthday
627:
Automorphic
Representations, L-Functions and Applications: Progress and Prospects: Proceedings of a Conference honoring Steve Rallis on the occasion of his 60th birthday
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Ginzburg, David; Jiang, Dihua; Rallis, Stephen (2009), "Models for certain residual representations of unitary groups. Automorphic forms and L-functions I.",
839:
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with David Ginzburg and David Soudry: On explicit lifts of cusp forms from GL(m) to classical groups. Annals of Mathematics (2) 150 (1999), no. 3, 807–866.
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with Avraham Aizenbud, Dmitry Gourevitch and Gerard Schiffmann: Multiplicity one theorems. Annals of Mathematics (2) 172 (2010), no. 2, 1407–1434.
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with Ilya Piatetski-Shapiro and Gerard Schiffmann: Rankin–Selberg integrals for the group G_2. Amer. J. Math. 114 (1992), no.6, 1269–1315.
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Ginzburg, David; Jiang, Dihua; Rallis, Stephen (2005), "On the nonvanishing of the central value of the Rankin–Selberg L-functions, II.",
739:
Ginzburg, David; Jiang, Dihua; Rallis, Stephen (2004), "On the nonvanishing of the central value of the Rankin–Selberg L-functions.",
725:
O'Connor, John J.; Robertson, Edmund F. "Stephen James Rallis," MacTutor History of Mathematics archive, University of St. Andrews (
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O'Connor, John J.; Robertson, Edmund F., "Ilya Piatetski–Shapiro", MacTutor History of Mathematics archive, University of St Andrews
259:
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In a series of papers between 2004 and 2009, David Ginzburg, Dihua Jiang, and Stephen Rallis proved one direction of the global
251:
and David Ginzburg wrote a series of papers culminating in their book "The descent map from automorphic representations of GL(
87:
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with Stephen Kudla: A regularized Siegel–Weil formula: the first term identity. Ann. Of Math. (2) 140 (1994), no. 1, 1–80.
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J. Cogdell and D. Jiang, coordinating eds., "Remembering Steve Rallis," Notices of the AMS 60 (2013), issue 4, 466–469
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J. Cogdell and D. Jiang, coordinating eds.,"Remembering Steve Rallis," Notices of the AMS 60 (2013), issue 4, 466–469
283:. His mathematical life was characterized by several long term collaborations with several mathematicians including
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227:. This led to Rallis's work with Kudla in which they developed a far-reaching generalization of the
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In 1990, Rallis gave an invited address on his work "Poles of Standard L-functions" at the 1990
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Langlands’ functoriality and the Weil representation. Amer.J.Math. 104 (1982), no. 3, 469–515.
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The L-functions studied by Rallis are important because of their connections with the
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J. Cogdell, H. Jacquet, D. Jiang, S. Kudla, (2015), eds. "Steve Rallis (1942–2012),"
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J. Cogdell, H. Jacquet, D. Jiang, S. Kudla, (2015), eds. "Steve Rallis (1942–2012),"
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J. Cogdell, H. Jacquet, D. Jiang, S. Kudla, (2015), eds. "Steve Rallis (1942–2012),"
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J. Cogdell, H. Jacquet, D. Jiang, S. Kudla, (2015), eds. "Steve Rallis (1942–2012),"
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388:: A tower of theta correspondences for G_2. Duke Math. J. 88 (1997), no. 3, 537–624.
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Beginning in the 1970s, Rallis and GĂ©rard Schiffmann wrote a series of papers on the
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Automorphic Representations, L-functions and Applications: Progress and Prospects
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The descent map from automorphic representations of GL(n) to classical groups
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344:: A new way to get Euler products. J.Reine Angew. Math. 392 (1988), 110–124.
331:: On the Weil–Siegel formula. J. Reine Angew. Math. 387 (1988), no. 1, 1–68.
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375:: Uniqueness of linear periods. Compositio Math. 387 (1996), no. 1, 65–123.
171:(May 17, 1942 – April 17, 2012) was an American mathematician who worked on
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On the Howe duality conjecture. Compositio Math. 51 (1984), no.3, 333–399.
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D. Bump (2005) "The Rankin–Selberg method: an introduction and survey" in
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Rallis's ideas had a significant and lasting impact on the theory of
788:, Providence, RI: Contemp. Math., 488, Amer. Math. Soc.: 125–146
414: + 1). Ann. of Math.(2) 157 (2003), no. 3, 891–917.
211:, and several visiting positions, he joined the faculty at
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in 1977 and stayed there for the rest of his career.
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467:Explicit constructions of automorphic L-functions
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442:L-functions and the oscillator representation
410:: On the nonnegativity of L(1/2,pi) for SO_2(
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201:Institute for Advanced Study in Princeton
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479:. World Scientific Publication Co. 2011.
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260:International Congress of Mathematicians
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299:Selected publications
213:Ohio State University
203:. After two years at
185:Langlands L-functions
173:group representations
132:Ohio State University
514:Robertson, Edmund F.
169:Stephen James Rallis
512:O'Connor, John J.;
229:Siegel–Weil formula
225:Weil representation
181:Siegel–Weil formula
103:automorphic descent
501:Notices of the AMS
445:. Springer. 1987.
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470:. Springer. 1987.
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177:automorphic forms
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157:Dihua Jiang
119:Mathematics
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52:17 May 1942
809:Categories
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