Collected Works 2000; 824 pp; hardcover Volume: 15 ISBN10: 082180930X ISBN13: 9780821809303 List Price: US$158 Member Price: US$126.40 Order Code: CWORKS/15
 This selection of papers of I. PiatetskiShapiro 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 PiatetskiShapiro'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. Readership Graduate students and research mathematicians. 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 Table of Contents Autobiographical papers  I. PiatetskiShapiro  Étude on life and automorphic forms in the Soviet Union
Early papers in harmonic analysis and number theory  I. I. PiatetskiShapiro  On the problem of uniqueness of the expansion of a function into a trigonometric series
 I. I. PiatetskiShapiro  On the distribution of prime numbers in sequences of the form \([f(n)]\)
 I. I. PiatetskiShapiro  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. PiatetskiiShapiro  Abelian modular functions
 I. I. PiatetskiiShapiro  On an estimate of the dimension of the space of automorphic forms for certain types of discrete groups
 I. I. PiatetskiShapiro  Discrete subgroups of the group of analytic automorphisms of the polycylinder and automorphic forms
 I. M. Gel'fand and I. I. PyateckiĭŠapiro  Theory of representations and theory of automorphic functions
 I. M. Gelfand and I. I. PjateckiĭŠapiro  Automorphic functions and representation theory
 I. I. PjateckiĭŠapiro  Automorphic functions and arithmetic groups
 I. I. PjateckiĭŠapiro  On reduction modulo a prime of fields of modular functions
 M. Gromov and I. PiatetskiShapiro  Nonarithmetic groups in Lobachevsky spaces
 P. Sarnak  Automorphic functions and discrete groups
Bounded homogeneous domains  I. I. PiatetskiShapiro  Some questions of harmonic analysis in homogeneous cones
 I. I. PiatetskiiShapiro  On a problem proposed by E. Cartan
 I. PyateckiĭŠapiro  Classification of bounded homogeneous domains in \(n\)dimensional complex space
 I. PjatetskiĭŠapiro  Bounded homogeneous domains in \(n\)dimensional complex space
 I. PjateckiĭŠapiro  Regions of the type of the upper halfplane in the theory of functions of several complex variables
 B. Vinberg, S. G. Gindikin, and I. I. PjateckiĭŠapiro  Classification and canonical realization of complex bounded homogeneous domains
 S. Gindikin  The work of PiatetskiShapiro on complex homogeneous bounded domains
Applied Mathematics  I. I. PyatetskiiShapiro, O. N. Stavskaya, and A. L. Toom  Automatic control in biological systems
 J. Cogdell and S. Gindikin  PiatetskiShapiro's work in applied mathematics
Algebraic geometry  I. I. PjateckiĭŠapiro and I. R. Šafarevič  A Torelli theorem for algebraic surfaces of type \(K3\)
 I. I. PjateckiĭŠapiro  Interrelations between the Tate and Hodge conjectures for abelian varieties
 I. I. PjateckiĭŠapiro and I. R. Šafarevič  The arithmetic of K3 surfaces
 P. Deligne  On the algebraic geometry papers of PiatetskiShapiro
Automorphic \(L\)functions  I. I. PjateckijŠapiro  On the WeilJacquetLanglands theorem
 I. I. PjateckijŠapiro  Euler subgroups
 S. S. Gelbart and I. I. PiatetskiShapiro  Automorphic \(L\)functions of halfintegral weight
 I. PiatetskiShapiro  Tate theory for reductive groups and distinguished representations
 H. Jacquet, I. I. PiatetskiShapiro, and J. Shalika  Automorphic forms on GL(3) I
 H. Jacquet, I. I. PiatetskiShapiro, and J. Shalika  Automorphic forms on GL(3) II
 H. Jacquet, I. I. PiatetskiShapiro, and J. Shalika  Relèvement cubique non normal
 H. Jacquet, I. I. PiatetskiiShapiro, and J. A. Shalika  RankinSelberg convolutions
 I. PiatetskiShapiro and S. Rallis  \(L\)functions of automorphic forms on simple classical groups
 S. J. Patterson and I. I. PiatetskiShapiro  A cubic analogue of the cuspidal theta representations
 I. PiatetskiShapiro and S. Rallis  A new way to get Euler products
 I. PiatetskiShapiro, S. Rallis, and G. Schiffmann  \(L\) functions for the group \(G_2\)
 J. W. Cogdell and I. I. PiatetskiShapiro  Converse theorems for GL\(_n\)
 J. Cogdell, S. Gelbart, and S. Rallis  The work of PiatetskiShapiro on \(L\)functions
Theta lifts and applications to generalized Ramanujan conjectures  R. Howe and I. I. PiatetskiShapiro  A counterexample to the "Generalized Ramanujan conjecture" for (quasi) split groups
 I. PiatetskiShapiro  Cuspidal automorphic representations associated to parabolic subgroups and Ramanujan conjecture
 I. I. PiatetskiShapiro  On the SaitoKurokawa lifting
 J.S. Li, I. PiatetskiShapiro, and P. Sarnak  Poincaré series for \(SO(n,1)\)
 J. W. Cogdell and I. I. PiatetskiShapiro  Unitarity and functoriality
 R. Howe and P. Sarnak  Theta lifts and applications to generalized Ramanujan conjectures
