Partitions and indefinite quadratic forms.

DOI10.1007/BF01388778zbMath0642.10012OpenAlexW2067062018MaRDI QIDQ1101143

Freeman J. Dyson, Dean R. Hickerson, George E. Andrews

Publication date: 1988

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143546

zbMATH Keywords

partitions arithmetic of quadratic field

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Theta series; Weil representation; theta correspondences (11F27) Elementary theory of partitions (11P81)

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Cites Work