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

✍ Scribed by Yuk-Kam Lau

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 169 KB
Volume: 80
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2436

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✦ Synopsis

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 tools: the Perron formula, the Parseval Theorem, and a Tauberian Theorem. The main difference between the present and the original method is that we include the contribution of the poles of the associated Dirichlet series on a certain line in the main term.

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