Selberg’s one-dimensional sieve with Buchstab weights of new type

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.     

Large Sieve Inequality with Quadratic Amplitudes

In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.     

Large Sieve Inequality with Quadratic Amplitudes

In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.     

Nonparametric Estimation of Regression Functions in Point Process Models

We prove that the empirical L ²-risk minimizing estimator over some general type of sieve classes is universally, strongly consistent for the regression function in a class of point process models of Poissonian type (random sampling processes). The universal consistency result needs weak assumptions on the underlying distributions and regression functions. It applies in particular to neural net classes and to radial basis function nets. For the estimation of the intensity functions of a Poisson process a similar technique yields consistency of the sieved maximum likelihood estimator for some general sieve classes. This revised version was published online in August 2006 with corrections to the Cover Date.     

An explicit sieve bound and small values of σ(ф(m))

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.     

Ⅱ型区间删失数据下广义部分线性模型的筛极大似然估计(英文)

This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.     

Sieve Estimates via Neural Network for Strong Mixing Processes

In this paper, we obtain the convergence rates of sieve estimates for α-mixing strictly stationary processes in the special case of neural networks. When the entropy of sieve satisfies certain conditions, we establish the bounds of sieve estimate. Using the bounds we give finally convergence rate of sieve estimate via neural networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

尖点形式L函数的广义零点密度估计(英文)

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.     

Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method

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.

     

一种Sieve极大似然估计的渐近性质

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．     

Ⅰ型区间删失情形下部分线性模型Sieve极大似然估计渐近性质

本文在响应变量的观测值为Ⅰ型区间删失数据的情形下,讨论部分线性模型Ｓｉｅｖｅ极大似然估计的渐近性质．在一定条件下证明了该估计具有强相合性;参数分量的估计具有渐近正态性,并且是渐近有效的;非参数分量估计达到了最优弱收敛速度．     

Discovery of a lost factoring machine

Despite the importance of the work of Eugène Carissan and the remarkable machine he built, very few people were aware of his work. Perhaps this was because both Pierre and Eugène died within 5 years of the exhibition of the machine in Paris in 1920. Indeed, when D. H. Lehmer began to construct his first automatic sieve in 1926, he had never heard of Carissan’s sieve, and he remained ignorant of it until 1989. Lehmer’s 1926 sieve, which was in some ways much less sophisticated than Carissan’s, made use of bicycle chains driven by an electric motor. It was his first attempt of many. Each time he built a new sieve, the most advanced technology was used: photoelectric cells in 1932,16-mm movie film in 1936, and delay lines in 1965 for the DLS-127 (later DLS-157). For an account of all of this, see [18].     

On a result of R. R. Hall

An upper bound for the mean value of a non-negative submultiplicative function by R. R. Hall [3] is sharpened and generalised. Hall's inequality implies a certain rather accurate upper sieve estimate, and this aspect of Hall's result is exploited in deriving good lower bounds for π(x) via the sieve.     

Sieve methods in combinatorics

We develop the Turán sieve and a ‘simple sieve’ in the context of bipartite graphs and apply them to various problems in combinatorics. More precisely, we provide applications in the cases of characters of abelian groups, vertex-colourings of graphs, Latin squares, connected graphs, and generators of groups. In addition, we give a spectral interpretation of the Turán sieve.     

A higher rank Selberg sieve and applications

We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.     

Zero-density estimates for automorphic <Emphasis Type="Italic">L</Emphasis>-functions

In this paper we prove zero-density estimates of the large sieve type for the automorphic L-function L（s, f × χ）, where f is a holomorphic cusp form and χ（mod q） is a primitive character.     

The segmented sieve of eratosthenes and primes in arithmetic progressions to 1012

The sieve of Eratosthenes, a well known tool for finding primes, is presented in several algorithmic forms. The algorithms are analyzed, with theoretical and actual computation times given. The authors use the sieve in a refined form (the dual sieve) to find the distribution of primes in twenty arithmetic progressions to 10¹². Tables of values are included.     

On twin primes associated with the Hawkins random sieve

We establish an asymptotic formula for the number of k-difference twin primes associated with the Hawkins random sieve, which is a probabilistic model of the Eratosthenes sieve. The formula for k=1 was obtained by M.C. Wunderlich [A probabilistic setting for prime number theory, Acta Arith. 26 (1974) 59-81]. We here extend this to k?2 and generalize it to all l-tuples of Hawkins primes.