共查询到20条相似文献,搜索用时 639 毫秒
1.
Liangyi Zhao 《Monatshefte für Mathematik》2007,151(2):165-173
In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish
non-trivial bounds. 相似文献
2.
We establish a result on the large sieve with square moduli. These bounds improve recent results by S. Baier [S. Baier, On the large sieve with sparse sets of moduli, J. Ramanujan Math. Soc. 21 (2006) 279-295] and L. Zhao [L. Zhao, Large sieve inequality for characters to square moduli, Acta Arith. 112 (3) (2004) 297-308]. 相似文献
3.
In this paper, we describe many improvements to the number field sieve. Our main contribution consists of a new way to compute individual logarithms with the number field sieve without solving a very large linear system for each logarithm. We show that, with these improvements, the number field sieve outperforms the gaussian integer method in the hundred digit range. We also illustrate our results by successfully computing discrete logarithms with GNFS in a large prime field.
4.
K.R. Matthews 《Journal of Number Theory》1973,5(1):16-23
The author observes that two Hermitian forms have the same largest eigenvalue. A large sieve result of Roth-Bombieri type and Selberg's upper bound sieve with a Montgomery type error term are derived. 相似文献
5.
E. Kowalski 《Archiv der Mathematik》2010,94(5):443-457
We give a new proof of the arithmetic large sieve inequality based on an amplification argument, and use a similar method
to prove a new sieve inequality for classical holomorphic cusp forms. A sample application of the latter is also given. 相似文献
6.
We prove an explicit sieve upper bound based on the large sieve of Montgomery and Vaughan [MV], and apply it to show that σ(ф(m)) ≥ m/39.4 for all positive integers m. 相似文献
7.
Jürgen G. Hinz 《Monatshefte für Mathematik》1985,100(4):259-275
Generalizing a method introduced by Elliott in the rational case to number fields in an appropriate way, asymptotic estimates are given for the number of algebraic primes in certain parallelotopes which are primitive roots for almost all (in a certain sense) prime ideal moduli. The proofs depend upon a fundamental lemma of Selberg's rational sieve method and make use of the large sieve in the setting of an algebraic number field. 相似文献
8.
Jianya Liu 《Mathematical Notes》2010,88(3-4):395-401
Enlarged major arcs in the Waring-Goldbach problem are studied by using large sieve estimates for Dirichlet polynomials and estimates for exponential sums over primes. 相似文献
9.
Gyan Prakash 《Journal of Number Theory》2009,129(2):428-433
We obtain a close to optimal version of the large sieve inequality with amplitudes given by the values of a polynomial with integer coefficients of degree ?2. 相似文献
10.
We prove variational forms of the Barban–Davenport–Halberstam Theorem and the large sieve inequality. We apply our result to prove an estimate for the sum of the squares of prime differences, averaged over arithmetic progressions. 相似文献
11.
In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L f (s,χ),where f is a holomorphic cusp form and χ a Dirichlet character of mod q. 相似文献
12.
Claus Bauer 《Frontiers of Mathematics in China》2017,12(2):261-280
We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic progressions. 相似文献
13.
14.
本文研究了大整数因子分解中的二次筛法,提出了算法选择,参数选择,硬件选取和过程控制上的优化途径,直接影响RSA密码系统,推动信息安全的发展。 相似文献
15.
Thorsten Kleinjung. 《Mathematics of Computation》2006,75(256):2037-2047
The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends on a good choice of a polynomial pair. In this article we present an improvement of the polynomial selection method of Montgomery and Murphy which has been used in recent GNFS records.
16.
Valentin Blomer 《Inventiones Mathematicae》2013,194(3):673-729
We develop a fairly explicit Kuznetsov formula on GL(3) and discuss the analytic behavior of the test functions on both sides. Applications to Weyl’s law, exceptional eigenvalues, a large sieve and L-functions are given. 相似文献
17.
18.
一种Sieve极大似然估计的渐近性质 总被引:2,自引:0,他引:2
该文针对部分线性模型,在响应变量的观测值为Ⅰ型区间删失数据的情形下,讨论Sieve极大似然估计的渐近性质.用三角级数来构造Sieve空间,在一定条件下证明了该估计具有强相合性;得到了该估计的弱收敛速度,并且非参数部分的估计达到了最优收敛速度;还算出了参数部分的信息界. 相似文献
19.
Goran Djankovi? 《Central European Journal of Mathematics》2012,10(2):748-760
In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality.
We investigate the family of GL
2 cusp forms modular with respect to the congruence subgroups Γ1(q), with additional averaging over the levels q ∼ Q. We obtain the orthogonality in the range N ≪ Q
2−δ
for any δ > 0, where N is the length of linear forms in the large sieve. 相似文献
20.
<正> 本文把数理方程研究中常用的嵌入定理稍作推广,应用到代数数域上来,并把[4]中第四章的定理4.2和[1,5]中的均值定理推广到代数数域上. 为此,先介绍一些符号与约定,基本上采自[2]. 设K为-n次代数数域,按通常的记号,记作n=r_1+2r_2.以Z_k表K中的整数环. 1.设为一理想,如α,β∈Z_k,|(α-β),则记α≡β(mod ).按此可把K中的整数分类,其类数为N.Z_k中与互素的整数在上述分类中占住类数为 相似文献