Results 21 to 30 of about 12,410,872 (300)
Mean values for a class of arithmetic functions in short intervals [PDF]
Mathematische Nachrichten, 2018 In this paper, we shall establish a rather general asymptotic formula in short intervals for a class of arithmetic functions and announce two applications about the distribution of divisors of square‐full numbers and integers representable as sums of two
Jie Wu, Qiang Wu
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On certain bounds for the divisor function [PDF]
Notes on Number Theory and Discrete MathematicsWe offer various bounds for the divisor function d(n), in terms of n, or other arithmetical functions.
József Sándor
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On certain arithmetical products involving the divisors of an integer [PDF]
Notes on Number Theory and Discrete MathematicsWe study the arithmetical products Π d^d, Πd^{1/d} and Πd^{log d}, where d runs through the divisors of an integer n>1.
József Sándor
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Teaching Arithmetic to Small Transformers [PDF]
arXiv.org, 2023 Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction ...
Nayoung Lee +4 more
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Inequalities between some arithmetic functions, II [PDF]
Notes on Number Theory and Discrete MathematicsAs a continuation of Part I (see [1]), we offer new inequalities for classical arithmetic functions such as the Euler's totient function, the Dedekind's psi function, the sum of the positive divisors function, the number of divisors function, extended ...
Krassimir Atanassov +2 more
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Chebyshev model arithmetic for factorable functions [PDF]
, 2016 This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating ...
Chachuat, B +3 more
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On certain inequalities for φ, ψ, σ and related functions, III [PDF]
Notes on Number Theory and Discrete MathematicsWe obtain generalizations of certain results from [2] and [4]. The unitary variants are also considered. Some new arithmetic functions and their inequalities are also considered.
József Sándor, Karol Gryszka
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Objects generated by an arbitrary natural number. Part 3: Standard modal-topological aspect [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [4], some arithmetic functions and arithmetic operators of a modal type are defined over the elements of Set(n).
Krassimir Atanassov
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CLASSIFICATION ON ARITHMETIC FUNCTIONS AND CORRESPONDING FREE-MOMENT L-FUNCTIONS
Bulletin of the Korean Mathematical Society, 2015 Ilwoo Cho
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Arithmetic functions at consecutive shifted primes [PDF]
, 2014 For each of the functions $f \in \{\phi, \sigma, \omega, \tau\}$ and every natural number $k$, we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots < f(p_{n+k}-1)$, and similarly for $f(p_n-1) > f(p_{n+1 ...
Pollack, Paul, Thompson, Lola
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