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Edmund Hlawka is a leading number theorist whose work has had a lasting influence on modern number theory and other branches of mathematics. He has contributed to diophantine approximation, the geometry of numbers, uniform distributions, analytic number theory, discrete geometry, convexity, numerical integration, inequalities, differential equations and gas dynamics. Of particular importance are his findings in the geometry of numbers (especially the Minkowski-Hlawka theorem) and uniform distribution. This Selecta volume collects his most important articles, many of which were previously hard to find. It will provide a useful tool for researchers and graduate students working in the areas covered, and includes a general introduction by E. Hlawka.
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Product Details

  • ISBN-13: 9780387506234
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 2/28/1990
  • Pages: 549
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.14 (d)

Table of Contents

Notes on the papers on geometry of numbers and on Diophantine approximations.- Über die Approximation von zwei komplexen inhomogenen Linearformen [3]*.- Über die Approximation von inhomogenen Linearformen [4].- Über komplexe homogene Linearformen [5].- Eine Ungleichung für Vektorlängen [6].- Zur Geometrie der Zahlen [7].- Ausfüllung und Überdeckung konvexer Körper durch konvexe Körper [16].- Über Gitterpunkte in Parallelepipeden [18].- Über Integrale auf konvexen Körpern I [19].- Über eine Klasse von mehrfachen Integralen [26].- Das inhomogene Problem in der Geometrie der Zahlen [30].- Über einen Satz von van der Corput [31].- Zur formalen Theorie der Gleichverteilung in kompakten Gruppen [32].- Folgen auf kompakten Räumen [33].- Zur Überdeckung der Ebene durch konvexe Scheiben [34].- Zum Hauptsatz der Theorie der Gleichverteilung [36].- Erbliche Eigenschaften in der Theorie der Gleichverteilung [40].- Funktionen von beschränkter Variation in der Theorie der Gleichverteilung [43].- Zur angenäherten Berechnung mehrfacher Integrale [45].- Rhythmische Folgen auf kompakten Gruppen I [46].- Zur Geometrie der Zahlen [49].- Discrepancy and uniform distribution of sequences [52].- Uniform distribution modulo 1 and numerical analysis [53].- Interpolation analytischer Funktionen auf dem Einheitskreis [60].- Ein metrischer Satz in der Theorie der C-Gleichverteilung [67].- Discrepancy and Riemann Integration [69].- Über eine Methode von E. Hecke in der Theorie der Gleichverteilung [74].- Mathematische Modelle der kinetischen Gastheorie [75].- Anwendung zahlentheoretischer Methoden auf Probleme der numerischen Mathematik I [80].- Über die Gleichverteilung gewisser Folgen, welche mit den Nullstellen der Zetafunktion zusammenhängen [83].- 90 Jahre Geometrie der Zahlen [92].- Approximation von Irrationalzahlen und pythagoräische Tripel [94].- Gleichverteilung auf Produkten von Sphären [102].- Eine Bemerkung zur Theorie der Gleichverteilung [109].- Carl Ludwig Siegel (31. 12. 1896–4.4. 1981) [117].- List of publications.- Acknowledgements.
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