Asymptotic expansion for the number of solutions of the diophantine system of Hilbert-Kamke with increasing number of variables

Journal of Mathematical Sciences - Tập 29 - Trang 1275-1289 - 1985
M. I. Israilov

Tài liệu tham khảo

G. I. Arkhipov, “The values of the singular series in the Hilbert-Kamke problem,” Dokl. Akad. Nauk SSSR,259, No. 2, 265–267 (1981). A. Bikyalis, “Multidimensional characteristic functions,” Litov. Mat. Sb.,8, No. 1, 21–39 (1968). A. Bikyalis, “Asymptotic expansion for the density and distribution of sums of independent random vectors with equal distribution,” Lit. Mat. Sb.,8, No. 3, 405–421 (1968). I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory, Interscience, London (1954) Sh. A. Ismatullaev, “A multidimensional additive problem with increasing number of terms,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk, No. 4, 16–20 (1974). M. I. Israilov, “On the Hurwitz zeta function,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat Nauk, No. 6, 13–18 (1981). G. Kramer, Random Vectors and Probability Distributions [in Russian], Moscow (1947). K. K. Mardzhanishvili, “Uniform distribution of n numbers as sums of complete first, second, ..., n-th powers,” Izv. Akad. Nauk SSSR, Ser. Mat.,4, 609–631 (1937). K. K. Mardzhanishvili, “On a system of diophantine equations,” Dokl. Akad. Nauk SSSR22, 471–474 (1939). A. G. Postnikov, “Additive problems with increasing number of terms,” Izv. Akad. Nauk SSSR, Ser. Mat.,20, No. 6, 751–764 (1956). S. Kh. Sirazhdinov and T. A. Azlarov, “On a theorem of A. G. Postnikov,” in: Limit Theorems of Probability Theory [in Russian], Izd. Akad. Nauk UzSSR, Tashkent (1963) pp 86–90. S. Kh. Sirazhdinov, T. A. Azlarov, and T. M. Zuparov, Additive Problems with Increasing Number of Terms [in Russian], Fan, Tashkent (1975). G. A. Freiman, “Waring's problem with increasing number of terms,” Uch. Zap. Elabuzh. Gos. Pedagog. Inst.,3, 120–137 (1953). A. N. Shiryaev, Probability [in Russian], Nauka, Moscow (1980). D. Castelnuovo, “Sur quelques problèmes se rattachant au calcul des probabilités,” Ann. Inst. H. Poincaré,3, 465–490 (1933). R. A. Rankin, “Representation of a number as sum of a large number of squares,” Proc. R. Soc. Edinburgh, Ser. A,65, 318–331 (1960–61).