Results 11 to 20 of about 3,057,361 (276)

The shifted prime-divisor function over shifted primes [PDF]

The Ramanujan Journal
Let a,b∈Z\{0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$a,b\in ...
K. Fan
semanticscholar   +4 more sources

Prime divisors of some shifted products [PDF]

International Journal of Mathematics and Mathematical Sciences, 2005
We study prime divisors of various sequences of positive integers A(n)+1, n=1,…,N, such that the ratios a(n)=A(n)/A(n−1) have some number-theoretic or combinatorial meaning.
Eric Levieil, Florian Luca, Igor E. Shparlinski   +2 more
doaj   +2 more sources

On shifted primes with large prime factors and their products [PDF]

Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013
We estimate from below the lower density of the set of prime numbers p such that p-1 has a prime factor of size at least p^c, where c lies in between 1/4 and 1/2.
F. Luca, Ricardo Menares, Amalia Pizarro-Madariaga   +2 more
semanticscholar   +6 more sources

Discrete uniform limit law for additive functions on shifted primes

Nonlinear Analysis, 2016
The sufficient and necessary conditions for a weak convergence of distributions of a set of strongly additive functions fx , x ⩾ 2, the arguments of which run through shifted primes, to the discrete uniform law are obtained. The case when fx (p) ∈ {0, 1}
Gediminas Stepanauskas, Laura Žvinytė
doaj   +2 more sources

Integers divisible by a large shifted prime [PDF]

Acta Arithmetica, 2016
Let $N(x,y)$ denote the number of integers $n\le x$ which are divisible by a shifted prime $p-1$ with $p>y$, $p$ prime. Improving upon recent bounds of McNew, Pollack and Pomerance, we establish the exact order of growth of $N(x,y)$ for all $x\ge 2y\ge 4$
Kevin Ford
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Long-term spatial dynamics of jaguars in a high-density population. [PDF]

PLoS ONE
We assessed the socio-spatial dynamics of a jaguar population over 15 years using camera-trap data from Belize. Using ~4,000 independent detections of male jaguars, we documented and quantified range shifts, overlap, and interactions between males ...
Bart J Harmsen, Rebecca J Foster
doaj   +2 more sources

Shifted primes without large prime factors [PDF]

Acta Arithmetica, 1998
Let \(\pi(x,y)=\sum_{\substack{ a {x \over (\log x)^c} , \] valid for an absolute constant \(c>0\), \(x\geq x_0(a)\), and \(y\geq x^\beta\) with \(\beta = 0.2961\). This improves on the result of \textit{J. B. Friedlander} [Number theory and applications, Proc. NATO ASI, Banff/Can. 1988, NATO ASI Ser., Ser.
R. Baker, G. Harman
semanticscholar   +3 more sources

On the density of shifted primes with large prime factors [PDF]

Science China Mathematics, 2017
As usual, denote byP(n) the largest prime factor of the integern>1 withthe conventionP(1) = 1. For 0< θ pθ}∣∣.In this paper, we obtain a new lower bound forTθ(x) asx→∞, which improves some recentresults of Luca-Menares-Madariaga (2015) and of Fengjuan Chen-Yonggao Chen (2016).
B. Feng, Jie Wu
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Multiplicative functions on shifted primes [PDF]

Journal of Number Theory, 2022
Let $f$ be a positive multiplicative function and let $k\geq 2$ be an integer. We prove that if the prime values $f(p)$ converge to $1$ sufficiently slowly as $p\rightarrow +\infty$, in the sense that $\sum_{p}|f(p)-1|=\infty$, there exists a real number $c>0$ such that the $k$-tuples $(f(p+1),\ldots,f(p+k))$ are dense in the hypercube $[0,c]^k$ or ...
openaire   +2 more sources

On values taken by the largest prime factor of shifted primes [PDF]

Journal of the Australian Mathematical Society, 2007
Denote by$\mathbb{P}$the set of all prime numbers and by$P(n)$the largest prime factor of positive integer$n\geq 1$with the convention$P(1)=1$. In this paper, we prove that, for each$\unicode[STIX]{x1D702}\in (\frac{32}{17},2.1426\cdots \,)$, there is a constant$c(\unicode[STIX]{x1D702})>1$such that, for every fixed nonzero integer$a\in \mathbb{Z}^{\
W. Banks, I. Shparlinski
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