On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s

M. A. Korolev

Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 7-49.

Résumé

An overview is given of the scientific results obtained by Anatolii Alekseevich Karatsuba between the early 1990s and 2008.

Détail

Keywords: prime number theorem, Riemann zeta function, divisor problem, exponential sums, Karatsuba's phenomenon, modular hyperbolas, Dirichlet characters, Kloosterman sums.
Mots-clés : fractional moments

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[72] A. A. Karatsuba, “On the zeros of arithmetic Dirichlet series without Euler product”, Russ. Acad. Sci., Izv. Math., 43:2 (1994), 193–203 | MR | MR | Zbl

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[80] A. A. Karatsuba, “Density theorem and the behavior of the argument of the Riemann zeta function”, Math. Notes, 60 (1996), 333–334 | DOI | DOI | MR | MR | Zbl

[81] A. A. Karatsuba, “Analogues of incomplete Kloosterman sums and their applications”, Tatra Mt. Math. Publ., 11 (1997), 89–120 | MR | Zbl

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