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Selected Works of Ilya Piatetski-Shapiro
Edited by: James Cogdell, Oklahoma State University, Stillwater, OK, Simon Gindikin, Rutgers University, Piscataway, NJ, and Peter Sarnak, Princeton University, NJ
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Collected Works
2000; 824 pp; hardcover
Volume: 15
ISBN-10: 0-8218-0930-X
ISBN-13: 978-0-8218-0930-3
List Price: US$158 Member Price: US$126.40
Order Code: CWORKS/15

Collected Works of Hervé Jacquet - Dorian Goldfeld

This selection of papers of I. Piatetski-Shapiro represents almost 50 years of his mathematical activity. Included are many of his major papers in harmonic analysis, number theory, discrete groups, bounded homogeneous domains, algebraic geometry, automorphic forms, and automorphic $$L$$-functions.

The papers in the volume are intended as a representative and accurate reflection of both the breadth and depth of Piatetski-Shapiro's work in mathematics. Some of his early works, such as those on the prime number theorem and on sets of uniqueness for trigonometric series, appear for the first time in English. Also included are several commentaries by his close colleagues. This volume offers an elegant representation of the contributions made by this renowned mathematician.

Reviews

"This is an impressive collection of papers by a mathematician of striking influence and originality. The editors are to be sincerely thanked for helping bring it to press. This volume will be a valuable and even inspirational addition to the desk or bookshelf of many a mathematician."

-- Mathematical Reviews

Autobiographical papers
• I. Piatetski-Shapiro -- Étude on life and automorphic forms in the Soviet Union
Early papers in harmonic analysis and number theory
• I. I. Piatetski-Shapiro -- On the problem of uniqueness of the expansion of a function into a trigonometric series
• I. I. Piatetski-Shapiro -- On the distribution of prime numbers in sequences of the form $$[f(n)]$$
• I. I. Piatetski-Shapiro -- An addition to the work "On the problem of uniqueness of the expansion of a function into a trigonometric series"
• P. Sarnak -- Early papers in harmonic analysis and number theory
Automorphic functions and discrete groups
• I. I. Piatetskii-Shapiro -- Abelian modular functions
• I. I. Piatetskii-Shapiro -- On an estimate of the dimension of the space of automorphic forms for certain types of discrete groups
• I. I. Piatetski-Shapiro -- Discrete subgroups of the group of analytic automorphisms of the polycylinder and automorphic forms
• I. M. Gel'fand and I. I. Pyateckiĭ-Šapiro -- Theory of representations and theory of automorphic functions
• I. M. Gelfand and I. I. Pjateckiĭ-Šapiro -- Automorphic functions and representation theory
• I. I. Pjateckiĭ-Šapiro -- Automorphic functions and arithmetic groups
• I. I. Pjateckiĭ-Šapiro -- On reduction modulo a prime of fields of modular functions
• M. Gromov and I. Piatetski-Shapiro -- Non-arithmetic groups in Lobachevsky spaces
• P. Sarnak -- Automorphic functions and discrete groups
Bounded homogeneous domains
• I. I. Piatetski-Shapiro -- Some questions of harmonic analysis in homogeneous cones
• I. I. Piatetskii-Shapiro -- On a problem proposed by E. Cartan
• I. Pyateckiĭ-Šapiro -- Classification of bounded homogeneous domains in $$n$$-dimensional complex space
• I. Pjatetskiĭ-Šapiro -- Bounded homogeneous domains in $$n$$-dimensional complex space
• I. Pjateckiĭ-Šapiro -- Regions of the type of the upper half-plane in the theory of functions of several complex variables
• B. Vinberg, S. G. Gindikin, and I. I. Pjateckiĭ-Šapiro -- Classification and canonical realization of complex bounded homogeneous domains
• S. Gindikin -- The work of Piatetski-Shapiro on complex homogeneous bounded domains
Applied Mathematics
• I. I. Pyatetskii-Shapiro, O. N. Stavskaya, and A. L. Toom -- Automatic control in biological systems
• J. Cogdell and S. Gindikin -- Piatetski-Shapiro's work in applied mathematics
Algebraic geometry
• I. I. Pjateckiĭ-Šapiro and I. R. Šafarevič -- A Torelli theorem for algebraic surfaces of type $$K3$$
• I. I. Pjateckiĭ-Šapiro -- Interrelations between the Tate and Hodge conjectures for abelian varieties
• I. I. Pjateckiĭ-Šapiro and I. R. Šafarevič -- The arithmetic of K3 surfaces
• P. Deligne -- On the algebraic geometry papers of Piatetski-Shapiro
Automorphic $$L$$-functions
• I. I. Pjateckij-Šapiro -- On the Weil-Jacquet-Langlands theorem
• I. I. Pjateckij-Šapiro -- Euler subgroups
• S. S. Gelbart and I. I. Piatetski-Shapiro -- Automorphic $$L$$-functions of half-integral weight
• I. Piatetski-Shapiro -- Tate theory for reductive groups and distinguished representations
• H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika -- Automorphic forms on GL(3) I
• H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika -- Automorphic forms on GL(3) II
• H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika -- Relèvement cubique non normal
• H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika -- Rankin-Selberg convolutions
• I. Piatetski-Shapiro and S. Rallis -- $$L$$-functions of automorphic forms on simple classical groups
• S. J. Patterson and I. I. Piatetski-Shapiro -- A cubic analogue of the cuspidal theta representations
• I. Piatetski-Shapiro and S. Rallis -- A new way to get Euler products
• I. Piatetski-Shapiro, S. Rallis, and G. Schiffmann -- $$L$$ functions for the group $$G_2$$
• J. W. Cogdell and I. I. Piatetski-Shapiro -- Converse theorems for GL$$_n$$
• J. Cogdell, S. Gelbart, and S. Rallis -- The work of Piatetski-Shapiro on $$L$$-functions
Theta lifts and applications to generalized Ramanujan conjectures
• R. Howe and I. I. Piatetski-Shapiro -- A counterexample to the "Generalized Ramanujan conjecture" for (quasi-) split groups
• I. Piatetski-Shapiro -- Cuspidal automorphic representations associated to parabolic subgroups and Ramanujan conjecture
• I. I. Piatetski-Shapiro -- On the Saito-Kurokawa lifting
• J.-S. Li, I. Piatetski-Shapiro, and P. Sarnak -- Poincaré series for $$SO(n,1)$$
• J. W. Cogdell and I. I. Piatetski-Shapiro -- Unitarity and functoriality
• R. Howe and P. Sarnak -- Theta lifts and applications to generalized Ramanujan conjectures