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.
Autobiographical papers: Etude on life and automorphic forms in the Soviet Union by I. Piatetski-Shapiro Early papers in harmonic analysis and number theory: On the problem of uniqueness of the expansion of a function into a trigonometric series by I. I. Piatetski-Shapiro On the distribution of prime numbers in sequences of the form $[f(n)]$ by I. I. Piatetski-Shapiro An addition to the work "On the problem of uniqueness of the expansion of a function into a trigonometric series" by I. I. Piatetski-Shapiro Early papers in harmonic analysis and number theory by P. Sarnak Automorphic functions and discrete groups: Abelian modular functions by I. I. Piatetskii-Shapiro On an estimate of the dimension of the space of automorphic forms for certain types of discrete groups by I. I. Piatetskii-Shapiro Discrete subgroups of the group of analytic automorphisms of the polycylinder and automorphic forms by I. I. Piatetski-Shapiro Theory of representations and theory of automorphic functions by I. M. Gel'fand and I. I. Pyateckii-Sapiro Automorphic functions and representation theory by I. M. Gelfand and I. I. Pjateckii-Sapiro Automorphic functions and arithmetic groups by I. I. Pjateckii-Sapiro On reduction modulo a prime of fields of modular functions by I. I. Pjateckii-Sapiro Non-arithmetic groups in Lobachevsky spaces by M. Gromov and I. Piatetski-Shapiro Automorphic functions and discrete groups by P. Sarnak Bounded homogeneous domains: Some questions of harmonic analysis in homogeneous cones by I. I. Piatetski-Shapiro On a problem proposed by E. Cartan by I. I. Piatetskii-Shapiro Classification of bounded homogeneous domains in $n$-dimensional complex space by I. Pyateckii-Sapiro Bounded homogeneous domains in $n$-dimensional complex space by I. Pjatetskii-Sapiro Regions of the type of the upper half-plane in the theory of functions of several complex variables by I. Pjateckii-Sapiro Classification and canonical realization of complex bounded homogeneous domains by E. B. Vinberg, S. G. Gindikin, and I. I. Pjateckii-Sapiro The work of Piatetski-Shapiro on complex homogeneous bounded domains by S. Gindikin Applied Mathematics: Automatic control in biological systems by I. I. Pyatetskii-Shapiro, O. N. Stavskaya, and A. L. Toom Piatetski-Shapiro's work in applied mathematics by J. Cogdell and S. Gindikin Algebraic geometry: A Torelli theorem for algebraic surfaces of type $K3$ by I. I. Pjateckii-Sapiro and I. R. Safarevic Interrelations between the Tate and Hodge conjectures for abelian varieties by I. I. Pjateckii-Sapiro The arithmetic of K3 surfaces by I. I. Pjateckii-Sapiro and I. R. Safarevic On the algebraic geometry papers of Piatetski-Shapiro by P. Deligne Automorphic $L$-functions: On the Weil-Jacquet-Langlands theorem by I. I. Pjateckij-Sapiro Euler subgroups by I. I. Pjateckij-Sapiro Automorphic $L$-functions of half-integral weight by S. S. Gelbart and I. I. Piatetski-Shapiro Tate theory for reductive groups and distinguished representations by I. Piatetski-Shapiro Automorphic forms on GL(3) I by H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika Automorphic forms on GL(3) II by H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika Relevement cubique non normal by H. Jacquet, I. I. Piatetski-Shapiro, and J. Shalika Rankin-Selberg convolutions by H. Jacquet, I. I. Piatetskii-Shapiro, and J. A. Shalika $L$-functions of automorphic forms on simple classical groups by I. Piatetski-Shapiro and S. Rallis A cubic analogue of the cuspidal theta representations by S. J. Patterson and I. I. Piatetski-Shapiro A new way to get Euler products by I. Piatetski-Shapiro and S. Rallis $L$ functions for the group $G 2$ by I. Piatetski-Shapiro, S. Rallis, and G. Schiffmann Converse theorems for GL$ n$ by J. W. Cogdell and I. I. Piatetski-Shapiro The work of Piatetski-Shapiro on $L$-functions by J. Cogdell, S. Gelbart, and S. Rallis Theta lifts and applications to generalized Ramanujan conjectures: A counterexample to the "Generalized Ramanujan conjecture" for (quasi-) split groups by R. Howe and I. I. Piatetski-Shapiro Cuspidal automorphic representations associated to parabolic subgroups and Ramanujan conjecture by I. Piatetski-Shapiro On the Saito-Kurokawa lifting by I. I. Piatetski-Shapiro Poincare series for $SO(n,1)$ by J.-S. Li, I. Piatetski-Shapiro, and P. Sarnak Unitarity and functoriality by J. W. Cogdell and I. I. Piatetski-Shapiro Theta lifts and applications to generalized Ramanujan conjectures by R. Howe and P. Sarnak.