Smoothing \Smooth" Numbers

نویسندگان

  • John B. Friedlander
  • Andrew Granville
چکیده

An integer is called y-smooth if all of its prime factors are y. An important problem is to show that the y-smooth integers up to x are equi-distributed amongst short intervals. In particular, for many applications we would like to know that if y is an arbitrarily small, xed power of x then all intervals of length p x, up to x, contain, asymptotically, the same number of y-smooth integers. We come close to this objective by proving that such y-smooth integers are so equi-distributed in intervals of length p xy 2+" , for any xed " > 0.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Self-Stabilizing Smoothing and Counting

A smoothing network is a distributed data structure that accepts tokens on input wires and routes them to output wires. It ensures that however imbalanced the traffic on input wires, the numbers of tokens emitted on output wires are approximately balanced. Prior work on smoothing networks always assumed that such networks were properly initialized. In a real distributed system, however, network...

متن کامل

Primitive Contractions of Calabi - Yau Threefolds

We construct examples of primitive contractions of Calabi–Yau threefolds with exceptional locus being P 1 ×P 1 , P 2 , and smooth del Pezzo surfaces of degrees ≤ 5. We describe the images of these primitive contractions and find their smoothing families. In particular we give a method to compute the Hodge numbers of a generic fiber of the smoothing familly of each Calabi–Yau threefold with one ...

متن کامل

Use of Two Smoothing Parameters in Penalized Spline Estimator for Bi-variate Predictor Non-parametric Regression Model

Penalized spline criteria involve the function of goodness of fit and penalty, which in the penalty function contains smoothing parameters. It serves to control the smoothness of the curve that works simultaneously with point knots and spline degree. The regression function with two predictors in the non-parametric model will have two different non-parametric regression functions. Therefore, we...

متن کامل

Some pitfalls in application of functional data analysis approach to association studies.

One of the most effective methods for gene-based mapping employs functional data analysis, which smoothes data using standard basis functions. The full functional linear model includes a functional representation of genotypes and their effects, while the beta-smooth only model smoothes the genotype effects only. Benefits and limitations of the beta-smooth only model should be studied before usi...

متن کامل

A MODIFICATION ON RIDGE ESTIMATION FOR FUZZY NONPARAMETRIC REGRESSION

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007