Geodesic
On types of solutions of the Lagrange problem
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 41-48.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we present an analysis of some cases where a positive integer cannot be represented by a diagonal quadratic form with four integer variables.
Keywords: quadratic form, trigonometric sum, comparison, Kloosterman sum, asymptotic formula.
Mots-clés : Gauss sum 
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L. N. Kurtova; N. N. Mot'kina. On types of solutions of the Lagrange problem. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part II, Tome 166 (2019), pp. 41-48. http://geodesic.mathdoc.fr/item/INTO_2019_166_a3/

[1] Malyshev A. V., “O predstavlenii tselykh chisel polozhitelnymi kvadratichnymi formami”, Tr. Mat. in-ta im. V. A. Steklova AN SSSR., 65 (1962), 3–212

[2] Estermann T., “On Kloosterman's sum”, Mathematica., 8 (1961), 83–86 | MR | Zbl

[3] Estermann T., “A new application of the Hardy–Littlewood–Kloosterman method”, Proc. London Math. Soc., 12 (1962), 425–444 | DOI | MR | Zbl

[4] Hua Loo-Keng, Introduction to Number Theory, Springer-Verlag, Berlin–Heidelberg–New York, 1982 | MR | Zbl

[5] Kloosterman H. D., “On the representation of number in the form”, Acta Math., 49 (1926), 407–464 | DOI | MR