Geometric and Analytic Number Theory

1. Front Matter

   Pages I-X

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2. The Dirichlet Approximation Theorem

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 1-18

3. The Kronecker Approximation Theorem

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 19-37

4. Geometry of Numbers

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 38-70

5. Number Theoretic Functions

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 71-105

6. The Prime Number Theorem

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 106-137

7. Characters of Groups of Residues

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 138-172

8. The Algorithm of Lenstra, Lenstra and Lovász

   • Edmund Hlawka, Rudolf Taschner, Johannes Schoißengeier

   Pages 173-183

9. Back Matter

   Pages 184-238

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In the English edition, the chapter on the Geometry of Numbers has been enlarged to include the important findings of H. Lenstraj furthermore, tried and tested examples and exercises have been included. The translator, Prof. Charles Thomas, has solved the difficult problem of the German text into English in an admirable way. He deserves transferring our 'Unreserved praise and special thailks. Finally, we would like to express our gratitude to Springer-Verlag, for their commitment to the publication of this English edition, and for the special care taken in its production. Vienna, March 1991 E. Hlawka J. SchoiBengeier R. Taschner Preface to the German Edition We have set ourselves two aims with the present book on number theory. On the one hand for a reader who has studied elementary number theory, and who has knowledge of analytic geometry, differential and integral calculus, together with the elements of complex variable theory, we wish to introduce basic results from the areas of the geometry of numbers, diophantine ap­ proximation, prime number theory, and the asymptotic calculation of number theoretic functions. However on the other hand for the student who has al­ ready studied analytic number theory, we also present results and principles of proof, which until now have barely if at all appeared in text books.

• Diophantine approximation
• Geometrie der Zahlen
• Prime
• Prime number
• Primzahlverteilung
• diophantische Approximation
• distribution of prime numbers
• geometry of numbers
• number theory

• Institut für Analysis, Technische Mathematik und Versicherungsmathematik, Technische Universität Wien, Wien, Austria

  Edmund Hlawka, Rudolf Taschner

• Institut für Mathematik, Universität Wien, Wien, Austria

  Johannes Schoißengeier

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