Geodesic
Number of lattice points in families of homothetic domains in $\mathbb{R}^n$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 17 (1983) no. 2, pp. 1-6.

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A. N. Varchenko. Number of lattice points in families of homothetic domains in $\mathbb{R}^n$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 17 (1983) no. 2, pp. 1-6. http://geodesic.mathdoc.fr/item/FAA_1983_17_2_a0/

[1] Colin de Verdier, “Nombre de points entiers dans une famille homo the tique de domaines de $R^n$”, Ann. Scient. Ecole Norm. Super., Ser. 4, 10:4 (1977), 559–575 | MR

[2] Randol B., “A lattice point problem I”, Trans. AMS, 121, 1966, 257–268 | DOI | MR | Zbl

[3] Randol B., “A lattice point problem II”, Trans. AMS, 125, 1966, 101–113 | DOI | MR | Zbl

[4] Randol B., “On the Fourier transform of the indicator function of the planar set”, Trans. AMS, 139, 1969, 271–278 | MR | Zbl

[5] Randol B., “On the asymptotic behaviour of the Fourier transform of the indicator function of a convex set”, Trans. AMS, 139, 1969, 279–285 | DOI | MR | Zbl

[6] Tarnopolska-Weiss M., “On the number of lattice points in a compact $n$-dimensional polyhedron”, Proc. Amer. Math. Soc., 74:1 (1979), 124–127 | DOI | MR | Zbl

[7] Giiemin V., Sternberg S., Geometricheskie asimptotiki, Mir, M., 1981 | MR

[8] Duistermaat J.J., “Oscillatory integrals, Lagrange immersions and unfolidngs of singularities”, Comm. Pure and Appl. Math., 27 (1974), 207–281 | DOI | MR | Zbl

[9] Godbiion K., Differentsialnaya geometriya i analiticheskaya mekhanika, Mir, M., 1973

[10] Karatsuba A.A., “Ivan Matveevich Vinogradov (k 90-letiyu so dnya rozhdeniya)”, UMN, 36:6 (1981), 3–16 | MR | Zbl

[11] Vinogradov I.M., Osobye varianty metoda trigonometricheskikh summ, Mir, M., 1976 | MR

[12] Khua-Lo-Gen, Metod trigonometricheskikh summ i ego primeneniya v teorii chisel, Mir, M., 1964 | MR

[13] Linnik Yu.V., Ergodicheskie svoistva algebraicheskikh polei, Izd. Leningr. un-ta, L., 1967 | MR

[14] Malyshev A.V., O predstavlenii tselykh chisel polozhitelnymi kvadratichnymi formami, Trudy MIAN im. V.A. Steklova, 65, 1962 | MR | Zbl

[15] Babenko K.I., “Ob asimptotike yadra Dirikhle sfericheskikh srednikh kratnykh ryadov Fure”, DAN SSSR, 243:5 (1978), 1097–1100 | MR | Zbl

[16] Konyagin S.V., “O tselykh tochkakh na strogo vypuklykh zamknutykh krivykh”, Matem. zametki, 21:6 (1977), 799–806 | MR | Zbl

[17] Jarnik V., “Über die Gitterpunkte auf konevexen Kurven”, Math. Zeit., 24 (1925), 500–518 | DOI | MR | Zbl

[18] Swinnerton-Dyer H.P.F., “The number of lattice points on a convex curve”, J. of Number Theory, 6 (1974), 128–135 | DOI | MR | Zbl

[19] Varchenko A.H., “O chisle tselykh tochek v oblasti”, UMN, 37:3 (1982), 177–178 | MR | Zbl