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Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
-
Noboru Ushiroya
Published/Copyright:
October 2, 2012
Abstract.
Let 
be an arithmetic function of n variables, where 
. We study the mean-value 
of f that is defined to be
if this limit exists. We first generalize the Wintner theorem and then consider the multiplicative case by expressing the mean-value as an infinite product over all prime numbers. In addition, we study the mean-value of a function of the form 
, where g is a multiplicative function of one variable, and express the mean-value by the Riemann zeta function.
Keywords: Mean-Value Theorem
Received: 2011-11-25
Revised: 2012-02-09
Accepted: 2012-04-22
Published Online: 2012-10-02
Published in Print: 2012-10-01
© 2012 by Walter de Gruyter Berlin Boston
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- The Googol-th Bit of the Erdős–Borwein Constant
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- Van der Waerden's Theorem on Homothetic Copies of {1,1+s,1+s+t}
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- A Proof of Catalan's Convolution Formula
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- The Impossibility of Certain Types of Carmichael Numbers
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- Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
- A Generalized Diagonal Wythoff Nim
- A Recursive Process Related to a Partizan Variation of Wythoff
- The (r1,...,rp)-Stirling Numbers of the Second Kind
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Keywords for this article
Mean-Value Theorem
Articles in the same Issue
- Masthead
- Two-Color Babylon
- On Abelian and Additive Complexity in Infinite Words
- Approximations of Additive Squares in Infinite Words
- The Googol-th Bit of the Erdős–Borwein Constant
- Odd Repdigits to Small Bases Are Not Perfect
- Enumeration of the Degree Sequences of Line-Hamiltonian Multigraphs
- The Characteristic Sequence and p-Orderings of the Set of d-th Powers of Integers
- Van der Waerden's Theorem on Homothetic Copies of {1,1+s,1+s+t}
- Sum-Products Estimates with Several Sets and Applications
- The 2-Adic, Binary and Decimal Periods of 1/3k Approach Full Complexity for Increasing k
- A Proof of Catalan's Convolution Formula
- Explicit Constructions of Large Families of Generalized More Sums Than Differences Sets
- The Impossibility of Certain Types of Carmichael Numbers
- Integer Subsets with High Volume and Low Perimeter
- Mean-Value Theorems for Multiplicative Arithmetic Functions of Several Variables
- A Generalized Diagonal Wythoff Nim
- A Recursive Process Related to a Partizan Variation of Wythoff
- The (r1,...,rp)-Stirling Numbers of the Second Kind
- Factor Frequencies in Languages Invariant Under Symmetries Preserving Factor Frequencies
- On k-Lehmer Numbers
