Strong wavefront lemma and counting lattice points in sectors |
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Authors: | Alexander Gorodnik Hee Oh Nimish Shah |
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Affiliation: | (1) LaGuardia Community College, 31-10 Thomson Avenue, Long Island City, NY 11101, USA;(2) Graduate Center of CUNY, 365 Fifth Avenue, New York, NY 10016, USA |
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Abstract: | We compute the asymptotics of the number of integral quadratic forms with prescribed orthogonal decompositions and more generally, the asymptotics of the number of lattice points lying in sectors of affine symmetric spaces. A new key ingredient in this article is the strong wavefront lemma, which shows that the generalized Cartan decomposition associated to a symmetric space is uniformly Lipschitz. |
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