Abstract
I shall discuss two results, which I obtained recently.
Similar content being viewed by others
Literature cited
L. Dirichlet, “Über die bestimmung der mittleren Werte in der Zahlentheorie,” Ann. Akad. Berlin (Werke, 2, 49–66) (1849), Math. Ann., 69–83.
G. Voronoi, “Sur un probléme du calcul des fonctions asymptotiques,” J. Math.,126, 241–282 (1903).
E. Landau, “Über die Anzahl der Gitterpunkte in gewissen Bereichen,” Nachr. Königl. Gesell. Wiss. Göttingen, Math.-Phys. Klassen, Hft.,6, 687–771 (1912).
G. H. Hardy and J. E. Littlewood, “The approximate functional equation in the theory of the zeta function, with applications to the division problems of Dirichlet and Piltz,” Proc. London Math. Soc. (2),21, 39–74 (1922).
I. M. Vinogradov, “A new estimate for (1+it),” Izv. Akad. Nauk SSSR, Ser. Math.,22, 161–164 (1958).
A. A. Karatsuba, “Estimates of trigonometric sums by the method of I. M. Vinogradov and their applications,” Proc. Math. Inst. Akad. Nauk SSSR,112, 241–255 (1971).
A. A. Karatsuba, “The Dirichlet divisor problem in number fields,” Dokl. Akad. Nauk SSSR,204, No. 3, 540–541 (1972).
A. A. Karatsuba, “A uniform estimate for the remainder term in the Dirichlet divisor problem,” Izv. Akad. Nauk SSSR, Ser. Math.,36, No. 3, 475–483 (1972).
I. M. Vinogradov, Collected Works, Izd. Akad. Nauk SSSR (1952).
A. A. Karatsuba, “Character sums and primitive roots in finite fields,” Dokl. Akad. Nauk SSSR,180, No. 6, 1287–1289 (1968).
A. A. Karatsuba, “Character sums with prime numbers,” Dokl. Akad. Nauk SSSR,190, No. 3, 517–518 (1970).
A. A. Karatsuba, “Character sums with prime numbers,” Izv. Akad. Nauk SSSR, Ser. Math.,34, No. 2, 299–321 (1970).
A. A. Karatsuba, “Distribution of products of shifted primes in arithmetic progressions,” Dokl. Akad. Nauk SSSR,192, No. 4, 724–727 (1970).
A. A. Karatsuba, “An arithmetical sum,” Dokl. Akad. Nauk SSSR,199, No. 4, 770–772 (1971).
A. A. Karatsuba, “Character sums with prime numbers belonging to an arithmetic progression,” Izv. Akad. Nauk SSSR, Ser. Math.,35, No. 3, 469–484 (1971).
A. A. Karatsuba, “Character sums in sequences of shifted primes, and their applications,” Matem. Zametki,17, No. 1, 155–159 (1975).
Additional information
Lecture read at the annual meeting of the mathematics section of the Academy of Science of the USSR.
Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 341–350, February, 1975.
Rights and permissions
About this article
Cite this article
Karatsuba, A.A. Some problems of contemporary analytic number theorem. Mathematical Notes of the Academy of Sciences of the USSR 17, 195–199 (1975). https://doi.org/10.1007/BF01161880
Issue Date:
DOI: https://doi.org/10.1007/BF01161880