Introduction to Diophantine Approximations

1. Front Matter

   Pages i-x

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2. General Formalism

   • Serge Lang

   Pages 1-19

3. Asymptotic Approximations

   • Serge Lang

   Pages 20-34

4. Estimates of Averaging Sums

   • Serge Lang

   Pages 35-49

5. Quadratic Irrationalities

   • Serge Lang

   Pages 50-68

6. The Exponential Function

   • Serge Lang

   Pages 69-77

7. Back Matter

   Pages 79-130

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The aim of this book is to illustrate by significant special examples three aspects of the theory of Diophantine approximations: the formal relationships that exist between counting processes and the functions entering the theory; the determination of these functions for numbers given as classical numbers; and certain asymptotic estimates holding almost everywhere.
Each chapter works out a special case of a much broader general theory, as yet unknown. Indications for this are given throughout the book, together with reference to current publications. The book may be used in a course in number theory, whose students will thus be put in contact with interesting but accessible problems on the ground floor of mathematics.

• Counting
• Diophantine approximation
• algebra
• approximation
• boundary element method
• continued fraction
• counting process
• distribution
• eXist
• exponential function
• form
• function
• functions
• number theory
• real number

• Department of Mathematics, Yale University, New Haven, USA

  Serge Lang

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