๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On the Existence of Limiting Distributions of Some Number-Theoretic Error Terms

โœ Scribed by Yuk-Kam Lau

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
147 KB
Volume
94
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

We prove the existence of the limiting distribution of a class of functions which are bounded and can be approximated by periodic functions in L 1 -norm. This had been investigated by Heath-Brown and our work is a generalization. A tool used here is the continuity theorem. By using its quantitative version, we can investigate the rate of convergence of some cases.

๐Ÿ“œ SIMILAR VOLUMES

On a Weighted Mean Square Result of the
On a Weighted Mean Square Result of the Error Terms of Some Arithmetical Functions
โœ Yuk-Kam Lau ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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

The Limit Distribution of a Number Theor
The Limit Distribution of a Number Theoretic Function Arising from a Problem in Statistical Mechanics
โœ Manfred Peter ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 151 KB

and for n # N, let 8(n) be the number of matrices C which are products of A's and B's where both A and B must occur, such that the trace tr(C)=n. It has been conjectured that This conjecture is disproved by showing that , has an absolutely continuous limit distribution with respect to the Lebesque