On the Karatsuba divisor problem
- Авторлар: Iudelevich V.V.1
-
Мекемелер:
- Lomonosov Moscow State University
- Шығарылым: Том 86, № 5 (2022)
- Беттер: 169-196
- Бөлім: Articles
- URL: https://journal-vniispk.ru/1607-0046/article/view/133901
- DOI: https://doi.org/10.4213/im9270
- ID: 133901
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
We obtain an upper bound for the sum$$\Phi_a(x) = \sum_{p\le x}\frac{1}{\tau(p+a)},$$where $\tau(n)$ is the divisor function, $a\ge 1$ is a fixed integer, and $p$ runs through primes up to $x$.
Негізгі сөздер
Авторлар туралы
Vitalii Iudelevich
Lomonosov Moscow State Universitywithout scientific degree, no status
Әдебиет тізімі
- E. C. Titchmarsh, “A divisor problem”, Rend. Circ. Mat. Palermo, 54 (1930), 414–429
- Ю. В. Линник, “Новые варианты и применения дисперсионного метода в бинарных аддитивных задачах”, Докл. АН СССР, 137:6 (1961), 1299–1302
- G. Rodriquez, “Sul problema dei divisori di Titchmarsh”, Boll. Un. Mat. Ital. (3), 20 (1965), 358–366
- H. Halberstam, “Footnote to the Titchmarsh–Linnik divisor problem”, Proc. Amer. Math. Soc., 18 (1967), 187–188
- E. Bombieri, J. B. Friedlander, H. Iwaniec, “Primes in arithmetic progressions to large moduli”, Acta Math., 156:3-4 (1986), 203–251
- E. Fouvry, “Sur le probleme des diviseurs de Titchmarsh”, J. Reine Angew. Math., 1985:357 (1985), 51–76
- S. Drappeau, B. Topacogullari, “Combinatorial identities and Titchmarsh's divisor problem for multiplicative functions”, Algebra Number Theory, 13:10 (2019), 2383–2425
- S. Ramanujan, “Some formulae in the analytic theory of numbers”, Messenger Math., 45 (1916), 81–84
- M. A. Korolev, “On Karatsuba's problem concerning the divisor function”, Monatsh. Math., 168:3-4 (2012), 403–441
- V. Kowalenko, “Properties and applications of the reciprocal logarithm numbers”, Acta Appl. Math., 109:2 (2010), 413–437
- С. М. Воронин, А. А. Карацуба, Дзета-функция Римана, Физматлит, М., 1994, 376 с.
- А. А. Карацуба, Основы аналитической теории чисел, Наука, М., 1975, 183 с.
- H. Halberstam, H.-E. Richert, Sieve methods, ed. Repint of the 1974 original, Dover Publ., Inc., Mineola, NY, 2011, 490 pp.
- J. Friedlander, H. Iwaniec, Opera de cribro, Amer. Math. Soc. Colloq. Publ., 57, Amer. Math. Soc., Providence, RI, 2010, xx+527 pp.
Қосымша файлдар
