Results 31 to 40 of about 381,379 (275)
Divisibility of arithmetic functions [PDF]
Pacific Journal of Mathematics, 1984 A derivative-like operator on the Dirichlet ring of arithmetic functions is used to develop formulas for the greatest common divisor of certain arithmetic functions. It is conjectured that formulas of this type hold more generally.
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A Functional Equation in Arithmetic [PDF]
Transactions of the American Mathematical Society, 1936 which occurs in all theories of numerical functions hitherto considered. The two most highly developed theories of this kind are those in which multiplication in the ring of all numerical functions is abstractly identical with C (Cauchy) or D (Dirichlet) multiplication of infinite series.t Lehmer's five postulates are sufficient for the development of ...
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Arithmetic functions associated with infinitary divisors of an integer
International Journal of Mathematics and Mathematical Sciences, 1993 The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y.
Graeme L. Cohen, Peter Hagis
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A Note about Iterated Arithmetic Functions [PDF]
, 2015 Let $f\colon\mathbb{N}\rightarrow\mathbb{N}_0$ be a multiplicative arithmetic function such that for all primes $p$ and positive integers $\alpha$, $f(p^{\alpha})
Defant, Colin
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Ray casting implicit fractal surfaces with reduced affine arithmetic [PDF]
, 2007 A method is presented for ray casting implicit surfaces defined by fractal combinations of procedural noise functions. The method is robust and uses affine arithmetic to bound the variation of the implicit function along a ray.
Gamito, M.N., Maddock, S.C.
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Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
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Privacy-Preserving Machine Learning With Fully Homomorphic Encryption for Deep Neural Network
IEEE Access, 2022 Fully homomorphic encryption (FHE) is a prospective tool for privacy-preserving machine learning (PPML). Several PPML models have been proposed based on various FHE schemes and approaches.
Joon-Woo Lee +10 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Let π(x) be the number of primes not exceeding x. We prove that π(x)
Bănescu Magdalena
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A note on the approximation of divisor functions [PDF]
Notes on Number Theory and Discrete MathematicsWe offer an arithmetic proof of a result from the recent paper [1]. A more general result is provided, too.
József Sándor
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Arithmetic of the Fabius Function
Integers, 2017 I solve here a question of Vladimir Reshetnikov in Mathoverflow (question 261649) about the values of Fabius function. Namely, I prove that the numbers $R_n:=2^{-\binom{n-1}{2}}(2n)! F(2^{-n})\prod_{m=1}^{\lfloor n/2\rfloor}(2^{2m}-1)$ are integers. We show also some other arithmetical properties of the values of Fabius function at dyadic points.
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