Results 1 to 10 of about 3,932 (162)
On an additive arithmetic function [PDF]
Let \(n\) be a positive integer, \(n=\prod\limits_{i=1}^rp_i^{\alpha_i}\) in canonical form, and let \(A(n)=\sum\limits_{i=1}^r\alpha_ip_i\). Clearly \(A\) is an additive arithmetic function.
Krishnaswami Alladi, P. Erdős
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On the distribution of arithmetic functions [PDF]
G. Jogesh Babu
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A simple proof of generalizations of number-theoretic sums [PDF]
For positive integers 𝑘, 𝑚, and 𝑛, let 𝑆𝑘 𝑚(𝑛) be the sum of all elements in the finite set {𝑥 𝑘 : 1 ≤ 𝑥 ≤ 𝑛⁄𝑚 , (𝑥, 𝑛) = 1}. The formula for 𝑆𝑘 𝑚(𝑛) is established and simpler formulae for 𝑆𝑘 𝑚(𝑛) under some conditions on 𝑚 and 𝑛 are verified. The
Yanapat Tongron+1 more
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Density of Arithmetic Representations of Function Fields [PDF]
We propose a conjecture on the density of arithmetic points in the deformation space of representations of the \'etale fundamental group in positive characteristic. This?
Hélène Esnault, Moritz Kerz
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ON A SUM INVOLVING CERTAIN ARITHMETIC FUNCTIONS ON PIATETSKI–SHAPIRO AND BEATTY SEQUENCES
Let 𝑐, 𝛼, 𝛽 ∈ R be such that ...
T. Srichan
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Math Can Be Visual—Teaching and Understanding Arithmetical Functions through Visualization
Number theory is an area of mathematics not unknown to students majoring in mathematics teaching. As early as in junior high, they may encounter basic number theory concepts such as prime numbers, multiples, divisors, or even the fundamental theorem of ...
Szilárd Svitek+2 more
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The local limit theorem of Delange in the Knopfmacher's semigroup
An asymptotic formula of the mean value of multiplicative arithmetic function from the class Ma(G) with asymptotical expansion of the main term is obtained. In the present paper the local limit theorem of the H. Delange type is proved.
Rimantas Skrabutėnas
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Asymptotical expansions in the Kubilius theorem of large deviations
In the present paper, a local theorem of large deviations for arithmetic functions defined in Knopfmacher’s semigroup is obtained.
Rimantas Skrabutėnas
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New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility
The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms.
Hsien-Chung Wu
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