James Cogdell

James Wesley Cogdell (* 1953 ) is an American mathematician.

He graduated from Yale University with a bachelor's degree in 1975 and received his doctorate there in 1981 under Ilja Pjatetskij-Shapiro ( Arithmetic Quotients of the Complex 2-Ball and Modular Forms of Nebypus ). He was a post-doctoral student at the University of Maryland and the University of California, Los Angeles . From 1982 to 1988 he was Assistant Professor at Rutgers University and from 1987 Assistant Professor, from 1988 Associate Professor and from 1994 Professor at Oklahoma State University (from 1999 as Southwestern Bell Professor, from 2000 as Regents Professor, from 2003 as Vaughan Foundation Professor ). From 2004 he is a professor at Ohio State University .

In 1983 and 1999/2000 he was at the Institute for Advanced Study and in 1988 at the Hebrew University. He was also visiting scholar at the University of Iowa , the Fields Institute and the Erwin Schrödinger Institute (Erwin Schrödinger Lecture 2009).

Cogdell deals with L-functions , automorphic representations ( Langlands program ), (analytical) number theory. In particular, he proved with Pjatetskij-Shapiro inverse theorems (Converse theorems) for L-functions of the general linear group . The aim is to characterize the L-functions that come from automorphic forms. For that was by Hervé Jacquet and Robert Langlands solved and by Jacquet, Piatetskij-Shapiro and Joseph Shalika . The problem goes back to Erich Hecke (characterization of the Dirichlet series that come from modular forms ). ${\displaystyle GL_{n}}$ ${\displaystyle GL_{2}}$ ${\displaystyle GL_{3}}$

In 2002 he was invited speaker at the International Congress of Mathematicians in Beijing ( Converse theorems, functoriality and applications to number theory , with Pjateskij-Shapiro). He was one of the editors of the selected works of his teacher Pyatetsky-Shapiro.

In 2012 he became a Fellow of the American Mathematical Society and in 2016 of the American Association for the Advancement of Science .

Fonts (selection)

• with Ilya Pjatetskij-Shapiro : The Arithmetic and Spectral Analysis of Poincaré Series (= Perspectives in Mathematics. 13). Academic Press, Boston MA et al. 1990, ISBN 0-12-178590-4 .
• with Ilya I. Pyatetskij-Shapiro: Converse theorems for . ${\displaystyle GL_{n}}$2 parts. (Part I): Publications Mathématiques de l'IHÉS. Volume 79, No. 1, 1994, pp. 157-214, ( online ); Part II: Journal for Pure and Applied Mathematics . Volume 507, 1999, pp. 165-188, doi : 10.1515 / crll.1999.507.165 .
• Analytic theory of functions for . Langlands conjectures for . Dual groups and Langlands functoriality. ${\displaystyle L}$ ${\displaystyle GL_{n}}$ ${\displaystyle GL_{n}}$In: Joseph Bernstein , Stephen Gelbart : An Introduction to the Langlands Program Birkhäuser, Boston MA et al. 2003, ISBN 0-8176-3211-5 , pp. 197-268.
• with Henry H. Kim, M. Ram Murty : Lectures on Automorphic Functions ${\displaystyle L}$ (= Fields Institute Monographs. 20). American Mathematical Society, Providence RI 2004, ISBN 0-8218-3516-5 .
• as editor with Dihua Jiang, Stephen S. Kudla , David Soudry, Robert J. Stanton: Automorphic Representations, -functions and Applications. Progress and Prospects. Proceedings of a Conference Honoring Steve Rallis on the Occasion of his 60th Birthday. The Ohio State University, March 27-30, 2003 ${\displaystyle L}$ (= Ohio State University Mathematical Research Institute Publications. 11). De Gruyter, Berlin et al. 2005, ISBN 3-11-017939-3 .
• ${\displaystyle L}$-functions and Converse Theorems for . ${\displaystyle GL_{n}}$In: Peter Sarnak , Freydoon Shahidi (Ed.): Automorphic Forms and Applications (= IAS / Park City Mathematics Series. 12). American Mathematical Society, Providence RI 2007, ISBN 978-0-8218-2873-1 , pp. 97-177.
• as editor with Jens Funke, Michael Rapoport , Tonghai Yang: Arithmetic Geometry and Automorphic Forms (= Advanced Lectures in Mathematics. 19). International Press et al., Somerville MA et al. 2011, ISBN 978-1-57146-229-9 .
  • Pp. 55–90: with Freydoon Shahidi : Some Generalized Functionals and Their Bessel Functions.
• as editor with Freydoon Shahidi, David Soudry (Eds.): Automorphic Forms and Related Geometry. Assessing the Legacy of II Piatetski-Shapiro. Conference on Automorphic Forms and Related Geometry: Assessing the Legacy of II Piatetski-Shapiro, April 23-27, 2012, Yale University, New Haven, CT (= Contemporary Mathematics . 614). American Mathematical Society, Providence RI 2014, ISBN 978-0-8218-9394-4 .
  • Pp. 31–51: Piatetski-Shapiro's Work on Converse Theorems.
  • Pp. 375-386: with Freydoon Shahidi, T.-L. Tsai: On Stability of Root Numbers.
• ${\displaystyle L}$-functions and non-abelian class field theory, from Artin to Langlands. In: Della Dumbaugh, Joachim Schwermer : Emil Artin and Beyond - Class Field Theory and -functions. ${\displaystyle L}$With Contributions by James Cogdell and Robert Langlands . European Mathematical Society, Zurich 2015, ISBN 978-3-03719-146-0 , pp. 127-161.

Web links

• Homepage

Individual evidence

1. ↑ James Cogdell in the Mathematics Genealogy Project (English)