Results 1 to 10 of about 48,609 (140)
On Complex Dimensions and Heat Content of Self-Similar Fractals
Fractal and FractionalComplex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics ...
William E. Hoffer, Michel L. Lapidus
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Approximation of classes of Poisson integrals by Fejer means
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2023 The work is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series.
O. G. Rovenska
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Approximation of analytic functions by repeated de la Vallee Poussin sums [PDF]
Компьютерные исследования и моделирование, 2019 The paper deals with the problems of approximation of periodic functions of high smoothness by arithmetic means of Fourier sums. The simplest and natural example of a linear process of approximation of continuous periodic functions of a real variable is ...
Olga G Rovenska
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On Certain Sums of Arithmetic Functions Involving the GCD and LCM of Two Positive Integers
Results in Mathematics, 2021 We obtain asymptotic formulas with remainder terms for the hyperbolic summations ∑mn≤xf((m,n))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Randell Heyman, L. Tóth
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Metric results on summatory arithmetic functions on Beatty sets [PDF]
Acta Arithmetica, 2019 Let $f\colon\mathbb{N}\rightarrow\mathbb{C}$ be an arithmetic function and consider the Beatty set $\mathcal{B}(\alpha) = \lbrace\, \lfloor n\alpha \rfloor : n\in\mathbb{N} \,\rbrace$ associated to a real number $\alpha$, where $\lfloor\xi\rfloor ...
Marc Technau, Agamemnon Zafeiropoulos
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Asymptotic convergence rates for averaging strategies [PDF]
Foundations of Genetic Algorithms, 2021 Parallel black box optimization consists in estimating the optimum of a function using λ parallel evaluations of f. Averaging the μ best individuals among the λ evaluations is known to provide better estimates of the optimum of a function than just ...
Laurent Meunier +3 more
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MEAN VALUES OF ARITHMETIC FUNCTIONS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS IN THE LARGE‐DEGREE LIMIT [PDF]
Mathematika, 2018 A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progression, with the interval as short as possible or the modulus as large as ...
O. Gorodetsky
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Short interval results for certain arithmetic functions [PDF]
, 2016 Using estimates on Hooley’s Δ-function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic functions over short segments. Numerous examples are also given.
O. Bordellès
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GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L ‐FUNCTIONS [PDF]
Mathematika, 2017 Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression.
G. Bhowmik +3 more
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Higher moments of arithmetic functions in short intervals: a geometric perspective [PDF]
, 2016 We study the geometry associated to the distribution of certain arithmetic functions, including the von Mangoldt function and the M\"obius function, in short intervals of polynomials over a finite field $\mathbb{F}_q$.
D. Hast, Vlad Matei
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