Results 1 to 10 of about 10,727,346 (343)
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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Grokking modular arithmetic [PDF]
arXiv.org, 2023 We present a simple neural network that can learn modular arithmetic tasks and exhibits a sudden jump in generalization known as ``grokking''. Concretely, we present (i) fully-connected two-layer networks that exhibit grokking on various modular ...
A. Gromov
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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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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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The local limit theorem of Delange in the Knopfmacher's semigroup
Lietuvos Matematikos Rinkinys, 2004 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
Lietuvos Matematikos Rinkinys, 2005 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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A Multivariate Arithmetic Function of Combinatorial and Topological Significance [PDF]
Integers, 2009 We investigate properties of a multivariate function E (m 1, m 2, …, m r), called orbicyclic, that arises in enumerative combinatorics in counting non-isomorphic maps on orientable surfaces.
V. Liskovets
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Certifying Zeros of Polynomial Systems Using Interval Arithmetic [PDF]
ACM Transactions on Mathematical Software, 2020 We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square
Paul Breiding, Kemal Rose, S. Timme
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New properties of arithmetic functions related to gcd and lcm [PDF]
Notes on Number Theory and Discrete MathematicsThis paper explores additional properties of the arithmetic functions f_α(n) and g_α(n), defined respectively by f_α(n)=Πʳᵢ₌₁pᵢ^{(eᵢ,α)} and g_α(n)=Πʳᵢ₌₁pᵢ^{[eᵢ,α]}, where n=Πʳᵢ₌₁pᵢ^eᵢ is the prime factorization of a positive integer n>1, (a,b) and [a,b]
Brahim Mittou
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