Andrzej Schinzel - Selecta, vol. I, II

Andrzej Schinzel is one of the leading figures and a living legend of contemporary mathematics. This selection of 100 of his papers shows the extraordinary variety of his mathematical interests. He wrote his first paper at the age of 17 and now the list contains more than 200 items. The central focus of his work is the arithmetic and algebraic properties of polynomials in one or several variables but as mentioned, this is only the tip of the iceberg, as shown by the fact that the selection is divided into 13 major sections, each devoted to a central theme and commented on by an expert. They include Diophantine equations and integral forms (10 papers, R. Tijdeman), continued fractions and integral forms (3 papers, E. Dubois), algebraic number theory (10 papers, D. W. Boyd and D. J. Lewis), polynomials in one variable (17 papers, M. Filaseta), polynomials in several variables (10 papers, U. Zannier), the Hilbert Irreducibility Theorem (3 papers, U. Zannier), arithmetic functions (6 papers, K. Ford), divisibility and congruences (11 papers, H.W. Lenstra Jr.), primitive divisors (6 papers, C. L. Stewart), prime numbers (5 papers, J. Kaczorowski), analytic number theory (4 papers, J. Kaczorowski), geometry of numbers (4 papers, W. M. Schmidt), and other papers (5 papers, S. Kwapien).

The selection ends with a chapter devoted to unsolved problems and unproved conjectures proposed by Schinzel up until 2006, which contains 56 items. The first, still open conjecture appeared in his 5th paper written in 1955 and concerns the decomposition of rationals into 3 unit (Egyptian) fractions. One of the most famous, the conjecture H, has the reference number 4. This extremely valuable collection of the most important papers of Andrzej Schinzel should certainly be on the shelf in every library.

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EUR 168