A combinatorial refinement of the Kronecker-Hurwitz class number relation
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- by Alexandru A. Popa and Don Zagier PDF
- Proc. Amer. Math. Soc. 145 (2017), 1003-1008 Request permission
Abstract:
We give a refinement of the Kronecker-Hurwitz class number relation, based on a tesselation of the Euclidean plane into semi-infinite triangles labeled by $\mathrm {PSL}_2(\mathbb {Z})$ that may be of independent interest.References
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- Adolf Hurwitz, Ueber Relationen zwischen Classenanzahlen binärer quadratischer Formen von negativer Determinante, Math. Ann. 25 (1885), no. 2, 157–196 (German). MR 1510301, DOI 10.1007/BF01446402
- L. Kronecker, Ueber die Anzahl der verschiedenen Classen quadratischer Formen von negativer Determinante, J. Reine Angew. Math. 57 (1860), 248–255 (German). MR 1579129, DOI 10.1515/crll.1860.57.248
Additional Information
- Alexandru A. Popa
- Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
- MR Author ID: 792375
- Email: alexandru.popa@imar.ro
- Don Zagier
- Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
- MR Author ID: 186205
- Email: don.zagier@mpim-bonn.mpg.de
- Received by editor(s): April 11, 2016
- Received by editor(s) in revised form: May 7, 2016
- Published electronically: September 15, 2016
- Additional Notes: The first author was partly supported by CNCSIS grant TE-2014-4-2077. He would like to thank the MPIM in Bonn and the IHES in Bures-sur-Yvette for providing support and a stimulating research environment while he was working on this paper.
- Communicated by: Kathrin Bringmann
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1003-1008
- MSC (2010): Primary 11E41
- DOI: https://doi.org/10.1090/proc/13281
- MathSciNet review: 3589300