Geodesic
The Linnik conjecture. The local approach
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 71-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Linnik sum is expanded in the spectrum by the local method. 
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A. I. Vinogradov. The Linnik conjecture. The local approach. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 11, Tome 319 (2004), pp. 71-80. http://geodesic.mathdoc.fr/item/ZNSL_2004_319_a2/

[1] Yu. V. Linnik, “Additive problems and eigenvalues modular operators”, Proc. of the International Congress of Math. (Stockholm, 1962), 1963, 217–284 | MR

[2] H. D. Kloosterman, “On the representation of numbers in the form $ax^2+by^2+cr^2+dt^2$”, Acta Math., 49 (1926), 407–464 | DOI | MR

[3] A. Weil, “On some exponential sums”, Proc. Nat. Acad. Sci. USA, 34 (1948), 204–207 | DOI | MR | Zbl

[4] A. Selberg, “On the estimation of Fourier coefficients of modular forms”, Proc. Symposia Pure Math., 8, Amer. Math. Sci., Providence, 1965, 1–15 | MR

[5] N. V. Kuznetsov, “Gipoteza Petersona dlya parabolicheskikh form vesa nul i gipoteza Linnika”, Matem. sb., 111:3 (1980), 334–383 | MR | Zbl

[6] I. M. Deshouillers, H. Iwaniec, “Kloostermann sums and Fourier coefficients of cusp form”, Invent. Math., 70 (1982), 219–288 | DOI | MR | Zbl

[7] D. Goldfeld, P. Sarnak, “Sums of Kloosterman Sums”, Invent. Math., 71 (1983), 243–250 | DOI | MR | Zbl

[8] A. I. Vinogradov, “O gipoteze Linnika”, Zap. nauchn. semin. POMI, 265, 1999, 64–76 | MR | Zbl

[9] A. I. Vinogradov, “$Z$-funktsiya Selberga. Lokalnyi podkhod”, Zap. nauchn. semin. POMI, 260, 1999, 298–316 | MR | Zbl