Diophantine Approximation
Roth's theorem, continued fractions, and subspace theorem.
Diophantine Approximation. Roth’s theorem, continued fractions, and subspace theorem.
Foundations and canonical references
The standard treatments of diophantine approximation approach the subject from complementary angles. Cassels, An Introduction to Diophantine Approximation (1957) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for diophantine approximation include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1957An Introduction to Diophantine Approximationcassels-1957
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