Geodesic
Pólya's conjecture in the presence of a constant magnetic field
Journal of the European Mathematical Society, Tome 11 (2009) no. 6, pp. 1365-1383.

Voir la notice de l'article provenant de la source EMS Press

We consider the Dirichlet Laplacian with a constant magnetic field in a two-dimensional domain of finite measure. We determine the sharp constants in semi-classical eigenvalue estimates and show, in particular, that Pólya's conjecture is not true in the presence of a magnetic field.
DOI : 10.4171/jems/184
Classification : 35-XX, 00-XX
Keywords: Eigenvalue bounds, semi-classical estimates, Pólya's conjecture, Laplace operator, magnetic Schrödinger operators. 
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     author = {Rupert L. Frank and Michael Loss and Timo Weidl},
     title = {P\'olya's conjecture in the presence of a constant magnetic field},
     journal = {Journal of the European Mathematical Society},
     pages = {1365--1383},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {2009},
     doi = {10.4171/jems/184},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/184/}
}
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Rupert L. Frank; Michael Loss; Timo Weidl. Pólya's conjecture in the presence of a constant magnetic field. Journal of the European Mathematical Society, Tome 11 (2009) no. 6, pp. 1365-1383. doi : 10.4171/jems/184. http://geodesic.mathdoc.fr/articles/10.4171/jems/184/

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