Piatetski-Shapiro primes from almost primes

Baker, R. C.; Banks, William D.; Guo, Zhenyu; Yeager, Aaron

doi:10.1007/s00605-013-0552-8

Cited by 18 publications

(9 citation statements)

References 10 publications

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“…‚ smooth, rough, and square-free numbers [1,2,6], ‚ almost-primes [7,9], ‚ additive problems [4,20,22], ‚ intersection with special sequences [3,5,8,13,19], and ‚ digital expansions [21,24,28]. For a broader picture of the scope of each topic, we refer the interested reader to the references within the cited items.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Kloosterman sums with twice-differentiable functions

Shparlinski¹,

Technau²

2020

Funct. Approx. Comment. Math.

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We bound Kloosterman-like sums of the shape N ÿ n"1 expp2πipxtf pnqu`ytf pnqu´1q{pq, with integers parts of a real-valued, twice-differentiable function f is satisfying a certain limit condition on f 2 , and tf pnqu´1 is meaning inversion modulo p.As an immediate application, we obtain results concerning the distribution of modular inverses inverses tf pnqu´1 pmod pq. The results apply, in particular, to Piatetski-Shapiro sequences tt c u with c P p1, 4 3 q. The proof is an adaptation of an argument used by Banks and the first named author in a series of papers from

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Kloosterman sums with twice-differentiable functions

Shparlinski¹,

Technau²

2020

Funct. Approx. Comment. Math.

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“…В 2011 г. Кай и Ван [3], улучшая более ранний результат Пеневой [4], показали, что если 1 < < 30/29, то существует бесконечно много простых чисел вида [ ] таких, что + 2 ∈ 5 . Позднее, в 2014 г., Бейкер, Банкс, Го и Йегер [5] показали, что если 1 < < 77/76, то последовательность…”

Section: введение и формулировка результатаunclassified

Number Theory and Applications, 2

Petrov¹,

Толев²,

Tolev³

2017

Sovrem. Probl. Mat.

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Общероссийский математический портал Ж. Х. Петров, Д. И. Толев, Об одном уравнении вклю-чающем дробные степени с одной простой и одной по-чти простой переменными, Совр. пробл. матем., 2017, выпуск 24, 46-65 DOI: https://doi.org/10.4213/spm68Использование Общероссийского математического портала Math-Net.Ru под-разумевает, что вы прочитали и согласны с пользовательским соглашением

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“…There is an extensive body of research on arithmetic functions with integer parts of real-valued functions, most commonly, with Beatty ⌊αn + β⌋ sequences, see, for example, [1,3,6,12,13], and Piatetski-Shapiro ⌊n γ ⌋ sequences, see, for example, [2,4,5,7,17,20], with real α, β and γ.…”

Section: Introductionmentioning

confidence: 99%