Transcendental Number Theory

ISBN-13: 9781009229944 / Angielski / Miękka / 2022 / 190 str.

Alan Baker

Opis

Alan Baker's systematic account of transcendental number theory, with a new introduction and afterword explaining recent developments.

Recenzje

'Baker's book is the book on transcendental numbers. He covers a majority of those areas that have reached definitive results, presents most of the proofs in a complete yet far more compact form than hitherto available, and covers historical and bibliographical matters with great thoroughness and impeccable scholarship. As literature, it compares well with the finest works of Landau, Rademacher, and Titchmarsh.' Kenneth B. Stolarsky, Bulletin of the American Mathematical Society

Spis treści

Introduction David Masser; Preface; 1. The origins; 2. Linear forms in logarithms; 3. Lower bounds for linear forms; 4. Diophantine equations; 5. Class numbers of imaginary quadratic fields; 6. Elliptic functions; 7. Rational approximations to algebraic numbers; 8. Mahler's classification; 9. Metrical theory; 10. The exponential function; 11. The Shiegel–Shidlovsky theorems; 12. Algebraic independence; Bibliography; Original papers; Further publications; New developments; Some Developments since 1990 David Masser; Index.