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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Intersection of modular polynomials


Author: Jie Ling
Journal: Proc. Amer. Math. Soc. 137 (2009), 1543-1549
MSC (2000): Primary 11G18, 14G35
Published electronically: November 12, 2008
MathSciNet review: 2470811
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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.


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Additional Information

Jie Ling
Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53705
Email: ling@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09750-5
PII: S 0002-9939(08)09750-5
Keywords: Intersection number, modular polynomial
Received by editor(s): June 18, 2008
Published electronically: November 12, 2008
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.