Representations of integers by an invariant polynomial and unipotent flows
Eskin, Alex ; Oh, Hee
Duke Math. J., Tome 131 (2006) no. 1, p. 481-506 / Harvested from Project Euclid
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We study a refined version of Linnik's problem on the asymptotic behavior of the number of representations of integers $m$ by an integral polynomial as $m$ tends to infinity. Assuming that the polynomials arise from invariant theory, we reduce the question to the study of limiting behavior of measures invariant under unipotent flows. Our main tool is then Ratner's theorem on the uniform distribution of unipotent flows, in a form refined by Dani and Margulis [DM2]
Publié le : 2006-12-01
Classification:  11D45,  37A45 
@article{1163170200,
     author = {Eskin, Alex and Oh, Hee},
     title = {Representations of integers by an invariant polynomial and unipotent flows},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 481-506},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163170200}
}

Eskin, Alex; Oh, Hee. Representations of integers by an invariant polynomial and unipotent flows. Duke Math. J., Tome 131 (2006) no. 1, pp.  481-506. http://gdmltest.u-ga.fr/item/1163170200/