WebPiatetski-Shaprio prime k-tuplet with exponent c. THEOREM. Let k^2begiven. Then, there for almost are infinitely all c>2, many Piatetski-Shapiro prime k-tuplets with exponent c. Remarks. The k cas = 2e follows from Balog's s resulto we may, assume k^ 3 henceforth. The exponen 2 ariset s from the proo off Lemma 3 below. If Web23 jan. 2024 · On the distribution of (k, r)-integers in Piatetski-Shapiro sequences Teerapat Srichan Mathematics Czechoslovak Mathematical Journal 2024 A natural number n is said to be a (k, r)-integer if n = akb, where k > r > 1 and b is not divisible by the rth power of any prime. We study the distribution of such (k, r)-integers in the… 1 PDF

kth powers in Piatetski-Shapiro sequences Article Information J …

Web1 mrt. 1992 · The well-known three primes theorem says that, for every sufficiently large odd integer N, the equation N=p1+p2+p3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}… Expand Save Alert Piatetski-Shapiro primes in arithmetic progressions Victor Z. Guo, Jinjia Li, M. Zhang Materials Science The Ramanujan … Web26 feb. 2010 · Piatetski-Shapiro [10] showed that there are infinitely many primes in this sequence for 1 < c < 12/11, obtaining the expected asymptotic formula for the number of such primes. The exponent 12/11 has been increased gradually by a number of authors to the present record 45/38 held by Kumchev [9]. ford racing bellhousing

Almost primes in Piatetski-Shapiro sequences - AIMS Mathematics

WebThe Piatetski-Shapiro sequence was introduced by Piatetski-Shapiro [9] to study prime numbers in a sequence of the form ⌊f(n)⌋, where f(n) is a polynomial. The study of the distribution of square-free and cube-free integers in Piatetski-Shapiro sequences has a long and rich history; see [2, 3, 4, 10, 12, 16]. The Webbers and Beatty sequences can be found in [10{12,15{17]. It is interesting to generalize the Piatetski{Shapiro sequences in the sense of Beatty sequences, since both Piatetski{Shapiro sequences and Beatty sequences produce in nitely many primes. Let 1 and be real numbers. We investigate the following generalized Piatetski{Shapiro … WebOn The Distribution of Consecutive Generalized r-FreeIntegers in Piatetski-Shapiro Sequences. ผู้แต่ง: Ms.angkana sripayap, Assistant Professor, Dr.teerapat srichan, … email passwords stored