Geodesic
Asymptotic estimates for spectral, bands of periodic Schr\"odenger operators
Algebra i analiz, Tome 17 (2005) no. 1, pp. 276-288.

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M. M. Skriganov; A. V. Sobolev. Asymptotic estimates for spectral, bands of periodic Schr\"odenger operators. Algebra i analiz, Tome 17 (2005) no. 1, pp. 276-288. http://geodesic.mathdoc.fr/item/AA_2005_17_1_a9/

[1] Götze F., “Lattice point problems and values of quadratic forms”, Invent. Math., 157 (2004), 145–226 | MR

[2] Helffer B., Mohamed A., “Asymptotic of the density of states for the Schrödinger operator with periodic electric potential”, Duke Math. J., 92 (1998), 1–60 | DOI | MR | Zbl

[3] Krätzel E., Lattice points, Math. Appl. (East European Ser.), 33, Kluwer Acad. Publ. Group, Dordrecht, 1988 | MR | Zbl

[4] Landau E., “Zur analytischen Zahlentheorie der definiten quadratischen Formen. (Über Gitterpunkte in einem mehrdimensionalen Ellipsoid)”, Berichte Math.-Natur. Kl. (Berlin), 31 (1915), 458–476

[5] Landau E., “Über Gitterpunkte in mehrdimensionalen Ellipsoiden”, Math. Z., 21 (1924), 126–132 | DOI | MR | Zbl

[6] Parnovski L., Sobolev A. V., “On the Bethe–Sommerfeld conjecture for the polyharmonic operator”, Duke Math. J., 107 (2001), 209–238 | DOI | MR | Zbl

[7] Parnovski L., Sobolev A. V., “Lattice points, perturbation theory and the periodic polyharmonic operator”, Ann. Henri Poincaré, 2 (2001), 573–581 | DOI | MR | Zbl

[8] Reed M., Simon B., Methods of modern mathematical physics. IV. Analysis of operators, Acad. Press, New York–London, 1978 | MR | Zbl

[9] Skriganov M. M., Geometricheskie i arifmeticheskie metody v spektralnoi teorii mnogomernykh periodicheskikh operatorov, Tr. Mat. in-ta AN SSSR, 171, 1985, 171 pp. | MR | Zbl

[10] Skriganov M. M., “The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential”, Invent. Math., 80 (1985), 107–121 | DOI | MR | Zbl

[11] Skriganov M. M., Sobolev A. V., Variation of the number of lattice points in large balls, Preprint, Univ. of Sussex, 2004