Results 1 to 10 of about 435,436 (131)
A simple proof of generalizations of number-theoretic sums [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2022 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]
Épijournal de Géométrie Algébrique, 2022 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
Проблемы анализа, 2022 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
Mathematics, 2022 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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Proofs, generalizations and analogs of Menon’s identity: a survey
Acta Universitatis Sapientiae: Mathematica, 2023 Menon’s identity states that for every positive integer n one has ∑ (a − 1, n) = φ (n)τ(n), where a runs through a reduced residue system (mod n), (a − 1, n) stands for the greatest common divisor of a − 1 and n, φ(n) is Euler’s totient function, and τ(n)
Tóth László
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New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility
Axioms, 2023 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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On a certain class of arithmetic functions [PDF]
Mathematica Bohemica, 2017 A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in\mathbb{N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general.
Antonio M. Oller-Marcén
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Exponential sums involving the divisor function over arithmetic progressions
AIMS Mathematics, 2023 Let $ \phi(x) $ be a smooth function supported on $ [1, 2] $ with derivatives bounded by $ \phi^{(j)}(x)\ll 1 $ and $ d_3(n) $ be the number of ways to write $ n $ as a product of three factors. We get the asymptotic formula for the nonlinear exponential
Rui Zhang , Yang Li, Xiaofei Yan
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Differentiability of the arithmetic volume function [PDF]
, 2008 We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle ...
Chen, Huayi
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On Certain Arithmetic Functions [PDF]
, 2000 In the recent book there appear certain arithmetic functions which are similar to the Smarandache function. In a recent paper we have considered certain generalization or duals of the Smarandache function.
Sandor, J.
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