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Some problems of contemporary analytic number theory. (English. Russian original) Zbl 0315.10039

Math. Notes 17, 195-199 (1975); translation from Mat. Zametki 17, 341-350 (1975).

MSC:

11N37 Asymptotic results on arithmetic functions
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11N69 Distribution of integers in special residue classes
11N35 Sieves
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References:

[1] L. Dirichlet, ?Über die bestimmung der mittleren Werte in der Zahlentheorie,? Ann. Akad. Berlin (Werke, 2, 49-66) (1849), Math. Ann., 69-83.
[2] G. Voronoi, ?Sur un probléme du calcul des fonctions asymptotiques,? J. Math.,126, 241-282 (1903). · JFM 34.0231.03
[3] E. Landau, ?Über die Anzahl der Gitterpunkte in gewissen Bereichen,? Nachr. Königl. Gesell. Wiss. Göttingen, Math.-Phys. Klassen, Hft.,6, 687-771 (1912). · JFM 43.0266.01
[4] 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). · JFM 48.1163.01 · doi:10.1112/plms/s2-21.1.39
[5] I. M. Vinogradov, ?A new estimate for (1+it),? Izv. Akad. Nauk SSSR, Ser. Math.,22, 161-164 (1958). · Zbl 0097.26302
[6] 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). · Zbl 0226.10037
[7] A. A. Karatsuba, ?The Dirichlet divisor problem in number fields,? Dokl. Akad. Nauk SSSR,204, No. 3, 540-541 (1972). · Zbl 0265.10011
[8] 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). · Zbl 0239.10025
[9] I. M. Vinogradov, Collected Works, Izd. Akad. Nauk SSSR (1952). · Zbl 0048.03104
[10] A. A. Karatsuba, ?Character sums and primitive roots in finite fields,? Dokl. Akad. Nauk SSSR,180, No. 6, 1287-1289 (1968). · Zbl 0182.37501
[11] A. A. Karatsuba, ?Character sums with prime numbers,? Dokl. Akad. Nauk SSSR,190, No. 3, 517-518 (1970).
[12] A. A. Karatsuba, ?Character sums with prime numbers,? Izv. Akad. Nauk SSSR, Ser. Math.,34, No. 2, 299-321 (1970).
[13] A. A. Karatsuba, ?Distribution of products of shifted primes in arithmetic progressions,? Dokl. Akad. Nauk SSSR,192, No. 4, 724-727 (1970). · Zbl 0224.10043
[14] A. A. Karatsuba, ?An arithmetical sum,? Dokl. Akad. Nauk SSSR,199, No. 4, 770-772 (1971).
[15] 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). · Zbl 0224.10038
[16] A. A. Karatsuba, ?Character sums in sequences of shifted primes, and their applications,? Matem. Zametki,17, No. 1, 155-159 (1975).
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