共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Given a sequence B of relatively prime positive integers with the sum of inverses finite, we investigate the problem of finding B-free numbers in short arithmetic progressions. 相似文献
3.
Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Π
p|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial
and the shifted powerful numbers.
Research supported in part by a grant from NSERC.
Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA.
Professor M.V. Subbarao passed away on February 15, 2006.
Received: 3 March 2006 Revised: 28 October 2006 相似文献
4.
Let p, q be primes and m be a positive integer. For a positive integer n, let ep(n) be the nonnegative integer with pep(n)|n and pep(n)+1?n. The following results are proved: (1) For any positive integer m, any prime p and any ε∈Zm, there are infinitely many positive integers n such that ; (2) For any positive integer m, there exists a constant D(m) such that if ε,δ∈Zm and p, q are two distinct primes with max{p,q}?D(m), then there exist infinitely many positive integers n such that , . Finally we pose four open problems. 相似文献
5.
On the distribution of square-full and cube-full integers 总被引:1,自引:0,他引:1
Jie Wu 《Monatshefte für Mathematik》1998,126(4):353-367
LetN
r
(x) be the number ofr-full integers x and let
r
(x) be the error term in the asymptotic formula forN
r
(x). Under Riemann's hypothesis, we prove the estimates 2(x)x1/7+, 3(x)x97/804+(>0), which improve those of Cao and Nowak. We also investigate the distribution ofr-full andl-free numbers in short intervals (r=2,3). Our results sharpen Krätzel's estimates. 相似文献
6.
Sophocles Mercourakis 《Monatshefte für Mathematik》1996,121(1-2):79-111
Two topics are investigated: countably determined (regular Borel probability) measures on compact Hausdorff spaces, and uniform distribution of sequences regarding mainly this kind of measures. We prove several characterizations of countably determined measures, and apply the results in order to show the existence of a well distributed sequence in the support of a countably determined measure. We also generalize a result of Losert on the existence of uniformly distributed sequences in compact dyadic spaces. 相似文献
7.
Byungchul Cha 《Journal of Number Theory》2010,130(4):1048-1055
We derive a formula for the density of positive integers satisfying a certain system of inequality, often referred as prime number races, in the case of the polynomial rings over finite fields. This is a function field analog of the work of Feuerverger and Martin, who established such formula in the number field case, building up on the fundamental work of Rubinstein and Sarnak. 相似文献
8.
Emre Alkan Andrew H. Ledoan Marian Vâjâitu Alexandru Zaharescu 《The Ramanujan Journal》2008,16(2):131-161
We prove asymptotic formulas for the first and second moments of the index of fractions with square-free denominators of order
Q streaming in a given arithmetic progression as Q→∞.
A. Zaharescu was supported by NSF grant number DMS-0456615.
This research was also partially supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research. 相似文献
9.
Vsevolod F. Lev 《Journal of Number Theory》2011,131(10):1827-1832
We prove that there is an absolute constant c>0 with the following property: if Z/pZ denotes the group of prime order p, and a subset A⊂Z/pZ satisfies 1<|A|<p/2, then for any positive integer there are at most 2m non-zero elements b∈Z/pZ with |(A+b)?A|?m. This (partially) extends onto prime-order groups the result, established earlier by S. Konyagin and the present author for the group of integers. We notice that if A⊂Z/pZ is an arithmetic progression and m<|A|<p/2, then there are exactly 2m non-zero elements b∈Z/pZ with |(A+b)?A|?m. Furthermore, the bound c|A|/ln|A| is best possible up to the value of the constant c. On the other hand, it is likely that the assumption can be dropped or substantially relaxed. 相似文献
10.
Melvyn B. Nathanson 《Journal of Number Theory》2009,129(6):1608-1621
The set of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If an∼αnh for some real number α>0, then α is called an additive eigenvalue of order h. The additive spectrum of order h is the set N(h) consisting of all additive eigenvalues of order h. It is proved that there is a positive number ηh?1/h! such that N(h)=(0,ηh) or N(h)=(0,ηh]. The proof uses results about the construction of supersequences of sequences with prescribed asymptotic growth, and also about the asymptotics of rearrangements of infinite sequences. For example, it is proved that there does not exist a strictly increasing sequence of integers such that bn∼n2 and B contains a subsequence such that bnk∼k3. 相似文献
11.
Yong-Gao Chen 《Journal of Number Theory》2003,98(2):310-319
In this paper we prove that if (r,12)?3, then the set of positive odd integers k such that kr−2n has at least two distinct prime factors for all positive integers n contains an infinite arithmetic progression. The same result corresponding to kr2n+1 is also true. 相似文献
12.
Yong-Gao Chen 《Journal of Number Theory》2003,100(2):326-331
Let p1,p2,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with
13.
In this note it is shown that if the connection integers of two maximal length FCSR sequences have a common prime factor,
then any crosscorrelation between them can be converted into some autocorrelation of the sequence with smaller period.
相似文献
14.
Laurenťiu Leuštean 《Central European Journal of Mathematics》2003,1(3):382-397
In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T
0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation
of a BL-algebra. 相似文献
15.
16.
We investigate the question of which growth rates are possible for the number of periodic points of a compact group automorphism. Our arguments involve a modification of Linnik?s Theorem, concerning small prime numbers in arithmetic progressions which lie in intervals. 相似文献
17.
K. Halupczok 《Acta Mathematica Hungarica》2008,120(4):315-349
We show that for every fixed A > 0 and θ > 0 there is a ϑ = ϑ(A, θ) > 0 with the following property. Let n be odd and sufficiently large, and let Q
1 = Q
2:= n
1/2(log n)−ϑ
and Q
3:= (log n)
θ
. Then for all q
3 ≦ Q
3, all reduced residues a
3 mod q
3, almost all q
2 ≦ Q
2, all admissible residues a
2 mod q
2, almost all q
1 ≦ Q
1 and all admissible residues a
1 mod q
1, there exists a representation n = p
1 + p
2 + p
3 with primes p
i
≡ a
i
(q
i
), i = 1, 2, 3.
相似文献
18.
Paul Vojta 《Journal of Number Theory》2007,125(1):229-234
In 1982-1983, E. Nochka proved a conjecture of Cartan on defects of holomorphic curves in Pn relative to a possibly degenerate set of hyperplanes. This was further explained by W. Chen in his 1987 thesis, and subsequently simplified by M. Ru and P.-M. Wong in 1991. The proof involved assigning weights to the hyperplanes. This paper provides further simplification of the proof of the construction of the weights, by bringing back the use of the convex hull in working with the “Nochka diagram.” 相似文献
19.
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
20.
Xue Gong Sun 《数学学报(英文版)》2010,26(1):155-160
Consider all the arithmetic progressions of odd numbers, no term of which is of the form 2^k + p, where k is a positive integer and p is an odd prime. ErdSs ever asked whether all these progressions can be obtained from covering congruences. In this paper, we characterize all arithmetic progressions in which there are positive proportion natural numbers that can be expressed in the form 2^k + p, and give a quantitative form of Romanoff's theorem on arithmetic progressions. As a corollary, we prove that the answer to the above Erdos problem is affirmative. 相似文献