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Showing 1 to 9 of 9 for “"Arithmetic functions"”.
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Some conditional results involving arithmetic functions
… conditional estimates on twisted sums of certain arithmetic functions such as generalized von Mangoldt and Mobius functions under the Riemann hypothesis, and we also present a strong converse. Second, we investigate a discrete negative moment of the zeta function, obtaining a lower bound that …
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Localization of Divisors of Integers and of Some Arithmetic Functions
We investigate several problems related to the multiplicative structure of integers. First, we determine the order of magnitude of the function H2(x, y, z), the number of positive integers n ≤ x having exactly two divisors in ( y, z], in the range of y10 ≤ z ≤ x1/3, and that of the …
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Uniform Distribution, Behrend Sequences, and Some Spaces of Arithmetic Functions
… third investigation focuses on a transform of arithmetic functions designed so that a density test set can be defined in terms of the action of the transform on characteristic functions. The domain of the transform is the set of functions that possess Ramanujan expansions. We establish several …
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Asymptotic formulae for certain arithmetic functions produced by fractional linear transformations
K.T. Atanassov introduced the two arithmetic functions \[ I(n) = \prod_{\nu=1}^k p_\nu^{1/\alpha_\nu} \qquad \text{and}\qquad R(n) = \prod_{\nu=1}^k p_\nu^{\alpha_v - 1} \] called the irrational factor and the strong restrictive factor, respectively. A variety of authors have studied the properties …
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Extensions of Selberg-Delange method
… determine the asymptotic behavior of the sum of arithmetic functions whose corresponding Dirichlet's series can be written in the term of the Riemann zeta function, $\zeta(s)$. In Chapter $2$, we first provide a history and recent developments of the Selberg-Delange method. Then, we provide a …
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Expectation Numbers of Cyclic Groups
… and dihedral groups. In chapter three we discuss arithmetic functions which are crucial to computing the first and second expectation numbers. The fourth chapter is where we introduce and prove asymptotic results for the first expectation number of large cyclic groups. The asymptotic results for …
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Efficient arithmetic for high speed DSP implementation on FPGAs
… there is a significant requirement for efficient arithmetic cores that utilises the resources on such devices. This thesis presents the research and development effort that was carried out to produce fixed point division and square root cores for use in a new Electronic Design Automation (EDA) …
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Computing with Spintronics: Circuits and architectures
… low-complexity logic implementations of various arithmetic functions. Spintastic establishes the synergy between stochastic computing and spin-based logic by demonstrating that they mutually alleviate each other's limitations. On the one hand, various building blocks of SC, which incur …
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O ensino do conteúdo Funções na escola de Ensino Médio José Paulo de França da cidade de Marí-PB: o que dizem os professores?
… investigating the teaching of content in school functions José Paulo School of France located in the city of Mari-PB from the conceptions of mathematics teachers. This research is a case study and is characterized by its descriptive character where we use the observation and questionnaires. The …