Properties of rational arithmetic functions
International Journal of Mathematics and Mathematical Sciences, 2005 Rational arithmetic functions are arithmetic functions of the form g1∗⋯∗gr∗h1−1∗⋯∗hs−1, where gi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied.
Vichian Laohakosol, Nittiya Pabhapote
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On a certain class of arithmetic functions [PDF]
Mathematica Bohemica, 2017 A homothetic arithmetic function of ratio $K$ is a function $f \mathbb{N}\rightarrow R$ such that $f(Kn)=f(n)$ for every $n\in\mathbb{N}$. Periodic arithmetic funtions are always homothetic, while the converse is not true in general.
Antonio M. Oller-Marcén
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Computing zeta functions of arithmetic schemes [PDF]
, 2015 We present new algorithms for computing zeta functions of algebraic varieties over finite fields. In particular, let X be an arithmetic scheme (scheme of finite type over Z), and for a prime p let zeta_{X_p}(s) be the local factor of its zeta function ...
Harvey, David
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On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L‐functions in the Selberg class [PDF]
Journal of the London Mathematical Society, 2015 We establish the equivalence of conjectures concerning the pair correlation of zeros of L ‐functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals.
H. Bui, J. Keating, D. Smith
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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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On certain arithmetic functions involving the greatest common divisor
Open Mathematics, 2012 Krätzel Ekkehard +2 more
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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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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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Applications of differential algebra to algebraic independence of arithmetic functions [PDF]
, 2015 We generalize and unify the proofs of several results on algebraic in- dependence of arithmetic functions and Dirichlet series by a theorem of Ax on differential Schanuel conjecture.
W. Pong
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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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