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On an arithmetic function
 J. London Math . Soc
, 1926
"... of sharp bounds on the distribution of a ..."
MATRICES AND CONVOLUTIONS OF ARITHMETIC FUNCTIONS
"... The purpose of this paper is to relate certain matrices with integer entries to convolutions of arithmetic functions. Let n be a positive integer, let a, 3, and y be arithmetic functions (complexvalued functions with domain the set of positive integers), and let ari ..."
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The purpose of this paper is to relate certain matrices with integer entries to convolutions of arithmetic functions. Let n be a positive integer, let a, 3, and y be arithmetic functions (complexvalued functions with domain the set of positive integers), and let ari
AVERAGE VALUES OF ARITHMETIC FUNCTIONS
"... Abstract. In this paper, we will present problems involving av erage values of arithmetic functions. The arithmetic functions we discuss are: (1)the number of representations of natural numbers as a sum of two squares and (2)as a sum of three squares, (3)the number of decompositions of natural numbe ..."
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Abstract. In this paper, we will present problems involving av erage values of arithmetic functions. The arithmetic functions we discuss are: (1)the number of representations of natural numbers as a sum of two squares and (2)as a sum of three squares, (3)the number of decompositions of natural
PROPERTIES OF RATIONAL ARITHMETIC FUNCTIONS
, 2005
"... Rational arithmetic functions are arithmetic functions of the form g1 ∗···∗gr ∗ h−1 1 ∗ ···∗h−1 s,wheregi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; ..."
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Rational arithmetic functions are arithmetic functions of the form g1 ∗···∗gr ∗ h−1 1 ∗ ···∗h−1 s,wheregi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established
VALUATIONS ON THE RING OF ARITHMETICAL FUNCTIONS
"... Abstract. In this paper we study a class of nontrivial independent absolute values on the ring A of arithmetical functions over the field C of complex numbers. We show that A is complete with respect to the metric structure obtained from each of these absolute values. We also consider an ArtinWhapl ..."
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Abstract. In this paper we study a class of nontrivial independent absolute values on the ring A of arithmetical functions over the field C of complex numbers. We show that A is complete with respect to the metric structure obtained from each of these absolute values. We also consider an Artin
On the binomial convolution of arithmetical functions
, 2008
"... Let n = ∏ p pνp(n) denote the canonical factorization of n ∈ N. The binomial convolution of arithmetical functions f and g is defined as (f ◦g)(n) = ∑ ( ∏ ( νp(n) dn p νp(d) f(d)g(n/d), where ..."
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Let n = ∏ p pνp(n) denote the canonical factorization of n ∈ N. The binomial convolution of arithmetical functions f and g is defined as (f ◦g)(n) = ∑ ( ∏ ( νp(n) dn p νp(d) f(d)g(n/d), where
Factorization of integers and arithmetic functions
, 2001
"... Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid’s proof for the fundamental theorem of arithmetic. 1. Introduction. In The Elements [11, BOOKS VII and IX] Euclid proved that, except for the order in which the factors are written, positive i ..."
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Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid’s proof for the fundamental theorem of arithmetic. 1. Introduction. In The Elements [11, BOOKS VII and IX] Euclid proved that, except for the order in which the factors are written, positive
Series involving Arithmetic Functions
, 2007
"... We intend here to collect infinite series, each involving unusual combinations or variations of wellknown arithmetic functions. For simplicity’s sake, results are often quoted not with full generality but only to illustrate a special case. Let σ(n) denote the sum of all distinct divisors of n, κ(n) ..."
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We intend here to collect infinite series, each involving unusual combinations or variations of wellknown arithmetic functions. For simplicity’s sake, results are often quoted not with full generality but only to illustrate a special case. Let σ(n) denote the sum of all distinct divisors of n, κ
Groups of Arithmetical Functions
"... An arithmetical function is a mapping from the positive integers to the complex numbers. The more interesting ones involve some numbertheoretic property, such as τ(n) = the number of positive divisors of n, σ(n) = the sum of the positive divisors of n, and φ(n) = the number of positive integers ..."
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Cited by 1 (0 self)
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An arithmetical function is a mapping from the positive integers to the complex numbers. The more interesting ones involve some numbertheoretic property, such as τ(n) = the number of positive divisors of n, σ(n) = the sum of the positive divisors of n, and φ(n) = the number of positive
Results 1  10
of
258,481