✦ LIBER ✦

On Differences of Twokth Powers: An Asymptotic Formula for the Mean-Square of the Error Term

✍ Scribed by M Kühleitner

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 195 KB
Volume: 76
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2352

No coin nor oath required. For personal study only.

✦ Synopsis

The arithmetic function r & k (n) counts the number of ways to write a natural number n as the difference of two kth powers (k 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of r & k (n) leads in a natural way to a certain error term 2 & k (t). In this article we prove an asymptotic formula for the mean-square of 2 & k (t).

📜 SIMILAR VOLUMES

On a Weighted Mean Square Result of the

On a Weighted Mean Square Result of the Error Terms of Some Arithmetical Functions

✍ Yuk-Kam Lau 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 169 KB

Let a(n) be an arithmetical function satisfying some conditions and write $ n x a(n)=main term+E(x). We obtain an asymptotic formula for a weighted mean square of the error term for some constants \_ 0 and c, by modifying a method that seems due to Titchmarsh. This method utilizes the following too

An Improvement on the Mean Value Formula

An Improvement on the Mean Value Formula for the Approximate Functional Equation of the Square of the Riemann Zeta-Function

✍ I. Kiuchi 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 143 KB

YouTube space as the propagative source

YouTube space as the propagative source for social power: An experimental study on the social meaning of disaster

✍ Aiko Takazawa 📂 Article 📅 2010 🏛 Wiley (John Wiley & Sons) 🌐 English ⚖ 225 KB