Higher dimensional Dedekind sums

DOI10.1007/BF01351173zbMath0237.10025MaRDI QIDQ2552517

Don Zagier

Publication date: 1973

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/162407

Mathematics Subject Classification ID

Trigonometric and exponential sums (general theory) (11L03)

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Cites Work

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• On the theory of Dedekind sums.
• Beziehungen zwischen Dedekindschen Summen
• Cohomologie-Operationen und charakteristische Klassen. (Cohomology operations and characteristic classes)
• Beispiele zur Differentialtopologie von Singularitäten
• The index of elliptic operators. III
• On Dedekind's transformation formula for \(\log\eta (\tau)\)
• Relations among invariants of circle actions on three-manifolds
• Equivariant Pontrjagin classes and applications to orbit spaces. Applications of the G-signature theorem to transformation groups, symmetric products and number theory
• Über die Bildung von Klasseninvarianten binärer quadratischer Formen mittels Dedekindscher Summen
• Über einige Anwendungen Dedekindscher Summen.
• Pseudo-Random Numbers: The Exact Distribution of Pairs
• On the Partition Function p (n )
• Theorems on Dedekind Sums