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An Asymptotic Formula for a Certain Mean Value in a Divisor Problem

✍ Scribed by Naoki Yanagisawa

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
296 KB
Volume
73
Category
Article
ISSN
0022-314X

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✦ Synopsis

An asymptotic formula for the mean square of the remainder term 2 a (x) is obtained for &10.
It is an interesting problem to obtain an asymptotic formula for the mean square of 2 a (x). It is known by Meurman [4] that
for &1Â2<a<0. This is an improvement on Kiuchi's former result [2], which gives the weaker error term O(X 5Â4+aÂ2+= ). Meurman [4] also proved that | X 0 2 &1Â2 (x) 2 dx=!(3Â2) 2 (24!(3)) &1 } X log X+O(X)

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