This book is an authoritative description of the various approaches to and methods in the theory of irregularities of distribution. The subject is primarily concerned with number theory, but also borders on combinatorics and probability theory. The work is in three parts. The first is concerned with the classical problem, complemented where appropriate with more recent results. In the second part, the authors study generalizations of the classical problem, pioneered by Schmidt. Here, they include chapters on the integral equation method of Schmidt and the more recent Fourier transform technique. The final part is devoted to Roth's '1/4-theorem'.
Part I. The Classical Problem: 1. Van der Corput's conjecture; 2. Lower bounds - Roth's method; 3. Upper bounds; 4. Lower bounds - a combinatorial method of Schmidt; Part II. Generalization of the Classical Problem: 5. Schmidt's work; 6. A Fourier transform approach; 7. Further applications of the Fourier transform method; 8. More upper bounds; Part III. More Problems!: 9. Miscellaneous questions.
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- ID: 9780521093002
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