共查询到20条相似文献,搜索用时 15 毫秒
1.
M. B. Khripunova 《Mathematical Notes》1998,63(5):658-669
The asymptotics of sums of the form Στ(|bn−a|) (summation overn<N, ω(n)=k) is studied, whereω(n) is the number of distinct prime divisors ofn, andτ(n) is the number of all divisors.
Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 749–762, May, 1998.
In conclusion, the author wishes to express his gratitude to Professor N. M. Timofeev for valuable advice.
This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-00502. 相似文献
2.
WeiLi Yao 《中国科学 数学(英文版)》2014,57(10):2103-2110
The purpose of this paper is to study the distribution of integers with a given number prime divisors over arithmetic progressions, via using the large-sieve inequality, Huxley-Hooley contour and the zero-density estimate, and present a Barban-Davenport-Halberstam type theorem for it. 相似文献
3.
M. A. Cherepnev 《Mathematical Notes》2006,80(5-6):863-867
The main result of this paper is the fact that the fraction of primes p ≤ x satisfying the condition that p ? 1 has a prime divisor q > exp(ln x/ln ln x) and the number of prime divisors of q ? 1 essentially differ from ln ln(x/n), where n = (p ? 1)/q, tends to zero as x increases. 相似文献
4.
5.
Chaohua Jia 《中国科学A辑(英文版)》2000,43(7):703-721
Suppose that α is an irrational number and β is a real number. It is proved that there are infinitely many prime numbers p
such that ‖ αp-β‖ <p
-9/28. 相似文献
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9.
Igor E. Shparlinski José Felipe Voloch 《Bulletin of the Brazilian Mathematical Society》2008,39(3):417-425
We view an algebraic curve over ℚ as providing a one-parameter family of number fields and obtain bounds for the average value
of some standard prime ideal counting functions over these families which are better than averaging the standard estimates
for these functions.
相似文献
10.
B. S. Kashin 《Mathematical Notes》2006,80(1-2):199-203
In this paper, a novel approach to the proof of inequalities of Lieb-Thirring type based on the standard apparatus of the theory of orthogonal series is proposed. 相似文献
11.
A. I. Pavlov 《Mathematical Notes》2000,68(3):370-377
The main result of this paper is the following theorem. Suppose thatτ(n) = ∑
d|n
l and the arithmetical functionF satisfies the following conditions:
Then there exist constantsA
1,A
2, andA
3 such that for any fixed \g3\s>0 the following relation holds:
. Moreover, if for any primep the inequality \vbf(p)\vb\s<1 holds and the functionF is strongly multiplicative, thenA
1\s>0.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 429–438, September, 2000. 相似文献
1) | the functionF is multiplicative; |
2) | ifF(n) = ∑ d|n f(d), then there exists an α>0 such that the relationf(n)=O(n −α) holds asn→∞. |
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13.
Bernd C. Kellner. 《Mathematics of Computation》2007,76(257):405-441
Let ( ) denote the usual th Bernoulli number. Let be a positive even integer where or . It is well known that the numerator of the reduced quotient is a product of powers of irregular primes. Let be an irregular pair with . We show that for every the congruence has a unique solution where and . The sequence defines a -adic integer which is a zero of a certain -adic zeta function originally defined by T. Kubota and H. W. Leopoldt. We show some properties of these functions and give some applications. Subsequently we give several computations of the (truncated) -adic expansion of for irregular pairs with below 1000.
14.
E. V. Vakhitova 《Mathematical Notes》1999,66(1):30-39
In this paper we study Selberg's sieve method with Buchstab weights of new type. The theorem proved in this paper gives a more advantageous choice of the parameters of a one-dimensional weighted sieve as compared to previous results. Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 38–49, July, 1999. 相似文献
15.
Koji Suzuki. 《Mathematics of Computation》2006,75(254):1015-1024
denotes the number of positive integers and free of prime factors . Hildebrand and Tenenbaum gave a smooth approximation formula for in the range , where is a fixed positive number . In this paper, by modifying their approximation formula, we provide a fast algorithm to approximate . The computational complexity of this algorithm is . We give numerical results which show that this algorithm provides accurate estimates for and is faster than conventional methods such as algorithms exploiting Dickman's function.
16.
Define to be the number of positive integers such that has no prime divisor larger than . We present a simple algorithm that approximates in floating point operations. This algorithm is based directly on a theorem of Hildebrand and Tenenbaum. We also present data which indicate that this algorithm is more accurate in practice than other known approximations, including the well-known approximation , where is Dickman's function.
17.
Ming Qiang WANG Xian Meng MENG 《数学学报(英文版)》2006,22(5):1329-1342
In this paper we prove that, with at most O(N^5/12+ε) exceptions, all positive odd integers n ≤ N with n ≡ 0 or 1(mod 3) can be written as a sum of a prime and two squares of primes. 相似文献
18.
Koji Suzuki. 《Mathematics of Computation》2004,73(246):1013-1022
denotes the number of positive integers and free of prime factors y$">. Hildebrand and Tenenbaum provided a good approximation of . However, their method requires the solution to the equation , and therefore it needs a large amount of time for the numerical solution of the above equation for large . Hildebrand also showed approximates for , where and is the unique solution to . Let be defined by for 0$">. We show approximates , and also approximates , where . Using these approximations, we give a simple method which approximates within a factor in the range , where is any positive constant.
19.
In 2020, Bergelson and Richter gave a dynamical generalization of the classical Prime Number Theorem, which has been generalized by Loyd in a disjoint form with the Erdős-Kac Theorem. These generalizations reveal the rich ergodic properties of the number of prime divisors of integers. In this article, we show a new generalization of Bergelson and Richter's Theorem in a disjoint form with the distribution of the largest prime factors of integers. Then following Bergelson and Richter's techniques, we will show the analogues of all of these results for the arithmetic semigroups arising from finite fields as well. 相似文献
20.
Stephan Hell 《Discrete and Computational Geometry》2008,40(4):586-594
Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of
Birch partitions: Evenness and a lower bound. This implies the first nontrivial lower bound for the number of Tverberg partitions
that holds for arbitrary q, where q is the number of partition blocks. The proofs are based on direct arguments and do not use the equivariant method from topological
combinatorics. 相似文献