# Andrzej Schinzel, Selecta

Volume I. Diophantine Problems and Polynomials

## Editors

### Henryk Iwaniec

Rutgers University, USA### Władysław Narkiewicz

University of Wrocław, Poland### Jerzy Urbanowicz

IM PAN, Warsaw, Poland

A subscription is required to access this book.

Andrzej Schinzel, born in 1937, is a leading number theorist whose work has a lasting impact on modern mathematics. He is the author of over 200 research articles in various branches of arithmetics, including elementary, analytic and algebraic number theory. He has also been, for nearly 40 years, the editor of Acta Arithmetica, the first international journal devoted exclusively to number theory.

These Selecta contain Schinzel's most important articles published between 1955 and 2006. The arrangement is by topic, with each major category introduced by an expert's comment. Many of the hundred selected papers deal with arithmetical and algebraic properties of polynomials in one or several variables, but there are also articles on Euler's totient function, the favorite subject of Schinzel's early research, on prime numbers (including the famous paper with Sierpiński on the Hypothesis “H”), algebraic number theory, diophantine equations, analytical number theory and geometry of numbers. Volume II concludes with some papers from outside number theory, as well as a list of unsolved problems and unproved conjectures, taken from the work of Schinzel.

pp. i–iv Frontmatterpp. v–vii Prefacepp. ix–xiv Contentsp. 1 Part A Diophantine equations and integral formspp. 3–126 Diophantine equations and integral formsp. 127 Part B Continued fractionspp. 129–166 Continued fractionsp. 167 Part C Algebraic number theorypp. 169–279 Algebraic number theoryp. 281 Part D Polynomials in one variablepp. 283–691 Polynomials in one variablep. 693 Part E Polynomials in several variablespp. 695–834 Polynomials in several variablesp. 835 Part F Hilbert’s Irreducibility Theorempp. 837–858 Hilbert’s Irreducibility Theorem