Intersection of modular polynomials
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- by Jie Ling PDF
- Proc. Amer. Math. Soc. 137 (2009), 1543-1549 Request permission
Abstract:
In this paper, we consider the intersection of classic modular polynomials. The intersection number on affine space is given by the well-known Hurwitz class numbers. We give two different ways to compute the intersection number by two different compactifications of $\mathbb {A}^2$. This yields a new and more elementary formula for the intersection number. Consequently we get a class number relation. We also give a pure combinatorial proof of this class number relation.References
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- Gunther Vogel, Modular polynomials, Astérisque 312 (2007), 1–7 (English, with English and French summaries). MR 2340366
Additional Information
- Jie Ling
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53705
- Email: ling@math.wisc.edu
- Received by editor(s): June 18, 2008
- Published electronically: November 12, 2008
- Communicated by: Wen-Ching Winnie Li
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1543-1549
- MSC (2000): Primary 11G18, 14G35
- DOI: https://doi.org/10.1090/S0002-9939-08-09750-5
- MathSciNet review: 2470811