DOI: 10.1007/978-3-642-15086-9_18. Special Variants of the Method of Trigonometric Sums

Special Variants of the Method of Trigonometric Sums

10.1007/978-3-642-15086-9_18

Crossref book-chapter

Springer Berlin Heidelberg

Selected Works (297)

Bibliography

Vinogradov, I. M. (1985). Special Variants of the Method of Trigonometric Sums. Selected Works, 299â383.

Authors 1

Ivan Matveevič Vinogradov (first)

References 28 Referenced 7

Vinogradov, I.M.: Fundamentals of Number Theory. Nauka, 1971 / Fundamentals of Number Theory by IM Vinogradov (1971)
Vinogradov, I.M.: The Method of Trigonometric Sums in Number Theory. 1971 / The Method of Trigonometric Sums in Number Theory by IM Vinogradov (1971)
Voronoi, G.: Sur un problème du calcul des fonctions asymptotiques. J. für Math., 126, 241–282, 1903 (in French) / J. für Math. by G Voronoi (1903)
Vinogradov, I.M.: A new method of deriving asymptotic expressions of arithmetic functions. Izv. Rossiiskoi Akademii Nauk, ser. 6, II, 1347–1378,1917 / Izv. Rossiiskoi Akademii Nauk, ser. by IM Vinogradov (1917)
Voronoi, G.: On a transcendental function and its applications in summation of certain sequences. Annales scientifiques de l’Ecole normale supérieure (3), XXI, 207–267, 1904 (10.24033/asens.539) / Annales scientifiques de l’Ecole normale supérieure (3) by G Voronoi (1904)
Hardy, G. H. and J. E. Littlewood: The trigonometrical series associated with the elliptic 5 function. Acta Math., 37, 193–239, 1914 (in English) (10.1007/BF02401834) / Acta Math. by GH Hardy (1914)
Vinogradov, I.M.: On the mean value of the number of classes of proper primitive forms of a negative discriminant. Soobshcheniya Khar’k. Matem. obshestva, 1918 (preprints dated 1917 came out of press the same year). / On the mean value of the number of classes of proper primitive forms of a negative discriminant / Soobshcheniya Khar’k. Matem. obshestva by IM Vinogradov (1918)
van der Corput, J.G.: Verschärfung der Abschätzungen beim Teileproblem. Math. Ann., 87, 39–65, 1922 (in German) (10.1007/BF01458035) / Math. Ann. by JG Corput van der (1922)
Hua, L. K.: The lattice points in a circle. Quart. J. Math., Oxford, 13, 18–29, 1942 (in English) (10.1093/qmath/os-13.1.18) / Quart. J. Math., Oxford by LK Hua (1942)
Vinogradov, I.M.: On the distribution of fractional parts of the values of a function of two variables. Izv. Leningradskogo Politekh. Instituta, 30, 31–52, 1927 / Leningradskogo Politekh. Instituta by IM Vinogradov (1927)
Vinogradov, I.M.: The number of integral points in a sphere. Trudy Matem. Instituta im. V.A. Steklova, AN SSSR, 9, 17–38, 1935 / Steklova, AN SSSR by IM Vinogradov (1935)
Vinogradov, I. M.: The number of integral points in a sphere. Izv. AN SSSR, 27, 957–968, 1963 / Izv. AN SSSR by IM Vinogradov (1963)
Hardy, G.H., and J.E. Littlewood: The approximate functional equation in the theory of the zeta-function with applications to the divisor problems of Dirichlet and Piltz. Proc. London Math. Soc. (2) 21, 39–74, 1922 (in English) / Proc. London Math. Soc. by GH Hardy (1922)
Karatsuba, A.A.: Estimates of trigonometric sums obtained by the Vinogradov method and their applications. Trudy ordena Lenina Matematicheskogo Instituta im. V.A. Steklova, CXII, Nauka, 1971, 241–255 / Estimates of trigonometric sums obtained by the Vinogradov method and their applications / Trudy ordena Lenina Matematicheskogo Instituta im. V.A. Steklova by AA Karatsuba (1971)
Vinogradov, I.M.: A new estimate of G(n) in Waring’s problem. Doklady AN SSSR, 5, 249–253, 1934 / Doklady AN SSSR by IM Vinogradov (1934)
Vinogradov, I.M.: The method of trigonometric sums in number theory. Trudy Matem. Instituta im. V.A. Steklova, 23, 1–109, 1947 / Trudy Matem. Instituta im. V.A. Steklova by IM Vinogradov (1947)
Vinogradov, I.M.: On the upper bound of G (n). Izv. AN SSSR, 29, 637–642, 1959 / Izv. AN SSSR by IM Vinogradov (1959)
Vinogradov, I.M.: New results on the distribution of fractional parts of a polynomial. Doklady AN SSSR, 2, 355–357, 1936 / Doklady AN SSSR by IM Vinogradov (1936)
Vinogradov, I.M.: Representation of an odd number as the sum of three primes. Doklady AN SSSR, 15, 291–294, 1937 / Doklady AN SSSR by IM Vinogradov (1937)
Vinogradov, I.M.: Estimates of certain simple trigonometric sums with prime numbers. Izv. AN SSSR, 3, 391–398, 1938 / Izv. AN SSSR by IM Vinogradov (1938)
Vinogradov, I.M.: Certain general properties of distribution of prime numbers. Matem. Sbornik, 7, 365–372, 1940 / Matem. Sbornik by IM Vinogradov (1940)
Vinogradov, I.M.: An improvement of the method for estimating sums over primes. Izv. AN SSSR, 7, 17–34, 1943 / Izv. AN SSSR by IM Vinogradov (1943)
Vinogradov, I.M.: Estimate of a sum taken over primes in an arithmetic progression. Izv. AN SSSR, 30, 481–496, 1966 / Izv. AN SSSR by IM Vinogradov (1966)
Karatsuba, A.A.: Sums of characters with primes. Izv. AN SSSR, 34, 299–321, 1970 / Izv. AN SSSR by AA Karatsuba (1970)
Page, A.: On the number of primes in arithmetic progression. Proc. London Math. Soc, (2) 39, 116–141, 1935 (in English) (10.1112/plms/s2-39.1.116) / Math. Soc, (2) by A Page (1935)
Mardzhanishvili, K.K.: On the proof of the Goldbach-Vinogradov theorem. Doklady AN SSSR, 30, 681–684, 1941 / Doklady AN SSSR by KK Mardzhanishvili (1941)
Vinogradov, I.M.: An elementary proof for a general assertion in analytical number theory. Izv. Leningradskogo Politekh. Instituta, 29, 3–12, 1925 / Izv. Leningradskogo Politekh. Instituta by IM Vinogradov (1925)
Vinogradov, I. M.: An elementary proof of a theorem in the theory of primes. Izv. AN SSSR, 17, 3–12, 1953 / Izv. AN SSSR by IM Vinogradov (1953)

Dates

Type	When
Created	11 years, 10 months ago (Oct. 21, 2013, 12:01 p.m.)
Deposited	6 years, 3 months ago (May 23, 2019, 2:32 p.m.)
Indexed	11 months, 2 weeks ago (Sept. 7, 2024, 7:49 p.m.)
Issued	40 years, 7 months ago (Jan. 1, 1985)
Published	40 years, 7 months ago (Jan. 1, 1985)
Published Print	40 years, 7 months ago (Jan. 1, 1985)

Funders 0

None

BibTeX

@inbook{Vinogradov_1985, title={Special Variants of the Method of Trigonometric Sums}, ISBN={9783642150869}, url={http://dx.doi.org/10.1007/978-3-642-15086-9_18}, DOI={10.1007/978-3-642-15086-9_18}, booktitle={Selected Works}, publisher={Springer Berlin Heidelberg}, author={Vinogradov, Ivan Matveevič}, year={1985}, pages={299–383} }

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