The Fractal Nature of an Approximate Prime Counting Function
Fractal and Fractional, 2017 Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function.
Dimitris Vartziotis, Joachim Wipper
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On distribution of the number of semisimple rings of order at most x in an arithmetic progression [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let ℓ and q denote relatively prime positive integers. In this article, we derive the asymptotic formula for the summation Σ_{n≤x, n≡ℓ (mod q)} S(n), where S(n) denotes the number of non-isomorphic finite semisimple rings with n elements.
Thorranin Thansri +2 more
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On certain inequalities for the prime counting function – Part III [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 As a continuation of [10] and [11], we offer some new inequalities for the prime counting function π(x). Particularly, a multiplicative analogue of the Hardy–Littlewood conjecture is provided. Improvements of the converse of Landau's inequality are given.
József Sándor
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Natural Lacunae Method and Schatten–Von Neumann Classes of the Convergence Exponent
Mathematics, 2022 Our first aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten–von Neumann class of ...
Maksim V. Kukushkin
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On the Quartic Residues and Their New Distribution Properties
Mathematics, 2020 In this paper, we use the analytic methods, the properties of the fourth-order characters, and the estimate for character sums to study the computational problems of one kind of special quartic residues modulo p, and give an exact calculation formula and
Juanli Su, Jiafan Zhang
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One Can Hear the Area of a Torus by Hearing the Eigenvalues of the Polyharmonic Operators
Demonstratio Mathematica, 2014 This paper considers the asymptotic properties for the spectrum of a positive integer power l of the Laplace-Beltrami operator acting on an n-dimensional torus T.
Guo Shunzi, Jin Jinyun
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The minimal growth of entire functions with given zeros along unbounded sets
Математичні Студії, 2020 Let $l$ be a continuous function on $\mathbb{R}$ increasing to $+\infty$, and $\varphi$ be a positive function on $\mathbb{R}$. We proved that the condition $$ \varliminf_{x\to+\infty}\frac{\varphi(\ln[x])}{\ln x}>0 $$ is necessary and sufficient in ...
I. V. Andrusyak, P.V. Filevych
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Enumeration Counting Formula Derivation of Binomial Tree Heap Based on Generating Function [PDF]
Jisuanji gongcheng, 2017 This paper proves that the enumeration counting recursion formula of max-heap is appliable to binomial tree heap(binomial tree that obeys the heap property) based on intensive study of the property of binomial heap.The enumeration number of binomial tree
LI Chao,SUN Qiang,ZHANG Zhujun
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Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts
Mathematics, 2021 For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the
Azmeer Nordin, Mohd Salmi Md Noorani
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Smart Count System Based on Object Detection Using Deep Learning
Remote Sensing, 2022 Object counting is an indispensable task in manufacturing and management. Recently, the development of image-processing techniques and deep learning object detection has achieved excellent performance in object-counting tasks.
Jiwon Moon +4 more
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