# Mean values for a class of arithmetic functions in short intervals

```@article{Wu2018MeanVF,
title={Mean values for a class of arithmetic functions in short intervals},
author={Jie Wu and Qiang Wu},
journal={Mathematische Nachrichten},
year={2018},
volume={293},
pages={178 - 202}
}```
• Published 24 July 2018
• Mathematics
• Mathematische Nachrichten
In this paper, we shall establish a rather general asymptotic formula in short intervals for a class of arithmetic functions and announce two applications about the distribution of divisors of square‐full numbers and integers representable as sums of two squares.
2 Citations
Materials Science
Czechoslovak Mathematical Journal
• 2022
Let K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}
Materials Science
Acta Mathematica Hungarica
• 2020
Assume that K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}
Mathematics
• 2014
In this paper, we establish a general mean value result of arithmetic functions over short intervals with the Selberg-Delange method. As an application, we generalize the
Mathematics
• 2019
In this paper, we establish a quite general mean value result of arithmetic functions over short intervals with the Selberg-Delange method and give some applications. In particular, we generalize
for some fixed A and B. Both (2) and (3) are proved by the use of mean value theorems, the large sieve in the case of (3). The lack of a bound for (1) which is good with respect to both Q and Tmay be
Mathematics
• 1974
In this the third memoir of the series we turn our attention to the following problems concerning the distribution of the numbers s that are expressible s the sum of two squares: — (i) the
Foreword Notation Part I. Elementary Methods: Some tools from real analysis 1. Prime numbers 2. Arithmetic functions 3. Average orders 4. Sieve methods 5. Extremal orders 6. The method of van der
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
Mathematics
• 1987
The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects
Update: This work reproduces an earlier result of Peck, which the author was initially unaware of. The method of the proof is essentially the same as the original work of Peck. There are no new
This is in continuation of the paper with the same title but with number IV. Theorem 6 of that paper reads as follows. Let 00 exp(((s)) 00 = :~::)nn-• and expexp(((s)) =L dnn-• n=l n=l in
While the results of Sathe's paper [J. Indian Math. Soc. 17 (1953), 63-141; 18 (1954), 27-81] are very beautiful and highly interesting, the way the author has proceeded in order to prove these