A generalisation of q-additive functions

Authors: Mišík, Ladislav^{j_ms-2025-0038_aff_001}, Porubský, Štefan^{j_ms-2025-0038_aff_002}

Source: Mathematica Slovaca. 75(3):525-536

Availability: https://www.degruyter.com/document/doi/10.1515/ms-2025-0038/html

On simply normal numbers with digit dependencies

Authors: Verónica Becher, Agustín Marchionna, Gérald Tenenbaum

Source: Mathematika. 69:988-991

Subject Terms: COMPLETELY ADDITIVE ARITHMETIC FUNCTION, Mathematics - Number Theory, NORMAL NUMBERS, TOEPLITZ SEQUENCES, Primary 11K16, 11N60, Secondary 11N56, FOS: Mathematics, Number Theory (math.NT), 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

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Access URL: http://arxiv.org/abs/2304.06850
http://hdl.handle.net/11336/219070

On addictive functions: On additive functions

Authors: Katai, I.

Source: Publicationes Mathematicae Debrecen. 25:251-257

Subject Terms: Arithmetic functions in probabilistic number theory, Additive Arithmetic Function, Arithmetic functions, related numbers, inversion formulas, Asymptotic Results, Asymptotic results on arithmetic functions, 0101 mathematics, 01 natural sciences, Abstract Theory of Number-Theoretic Functions

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Access URL: https://zbmath.org/3611442

On the characterization of additive functions on rare sets

Authors: Kovács, K.

Source: Publicationes Mathematicae Debrecen. 40:137-141

Subject Terms: vector-valued functions, additive arithmetic function, rare sets, Rate of growth of arithmetic functions, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/55019

ASYMPTOTICS OF PROBABILITY CHARACTERISTICS OF ADDITIVE ARITHMETIC FUNCTIONS

Source: Прикладная физика и математика.

Subject Terms: асимптотика вероятностных характеристик арифметических функций, additive arithmetic function, аддитивная арифметическая функция, strongly additive arithmetic function, арифметическая функция, asymptotics of probabilistic characteristics of arithmetic functions, сильно аддитивная арифметическая функция, arithmetic function

ESTIMATE OF ASYMPTOTICS OF THE MOMENTS OF ARITHMETIC FUNCTIONS HAVING A LIMITING DISTRIBUTION

Source: Прикладная физика и математика.

Subject Terms: additive arithmetic function, предельное распределение, аддитивная арифметическая функция, вероятностное пространство, strongly additive arithmetic function, analogue of the law of large numbers, limit distribution, последовательность случайных величин, independence of random variables, probability space, sequence of random variables, аналог закона больших чисел, центральный момент k-ого порядка, central moment of the k-th order, asymptotics of the moments of arithmetic functions, асимптотики моментов арифметических функций, независимость случайных величин, арифметическая функция, сильно аддитивная арифметическая функция, arithmetic function

ESTIMATE OF THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF ARITHMETIC FUNCTIONS HAVING LIMITING NORMAL DISTRIBUTION

Source: Прикладная физика и математика.

Subject Terms: additive arithmetic function, normal distribution, предельное распределение, аддитивная арифметическая функция, вероятностное пространство, strongly additive arithmetic function, analogue of the law of large numbers, Центральная предельная теорема, limit distribution, Central limit theorem, последовательность случайных величин, independence of random variables, probability space, sequence of random variables, аналог закона больших чисел, asymptotics of moments of arithmetic functions, асимптотики моментов арифметических функций, независимость случайных величин, арифметическая функция, сильно аддитивная арифметическая функция, arithmetic function, нормальное распределение

SOME QUESTIONS OF PROBABILISTIC NUMBER THEORY

Source: Прикладная физика и математика.

Subject Terms: неравенство Чебышева, asymptotic law of prime numbers, асимптотический закон простых чисел, решето Эратосфена, предельная функция распределения, вероятностное пространство, analogue of the law of large numbers, standard function normal distribution, последовательность случайных величин, asymptotics of probabilistic characteristics of arithmetic functions, density of a subset of natural series, probability space, функция стандартного нормального распределения, асимптотики вероятностных характеристик арифметических функций, количество простых делителей натурального числа, arithmetic function, sieve of Eratosthenes, asymptotic density, limit distribution function, Mertens theorem, strongly additive arithmetic function, теорема Мертенса, independence of random variables, sequence of random variables, number of prime divisors of natural number, асимптотическая плотность, аналог закона больших чисел, Chebyshev inequality, независимые события, плотность подмножества натурального ряда, независимость случайных величин, арифметическая функция, сильно аддитивная арифметическая функция, independent events

Discrete uniform distribution for a sum of additive functions

Authors: Stepanauskas, Gediminas, Žvinytė, Laura

Source: Lithuanian Mathematical Journal. :1-10

A Turan--Kubilius type inequality on shifted products

Authors: Rivat, Joel, Sarkozy, Andras

Contributors: I2m, Aigle

Source: Publicationes Mathematicae Debrecen. :637-662

Subject Terms: additive arithmetic function, probabilistic number theory, multiplicative characters, shifted product, large sieve, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

Access URL: https://dialnet.unirioja.es/servlet/articulo?codigo=3848018
https://hal.archives-ouvertes.fr/hal-01260134

NOTES ON ERDÖS’ CONJECTURE: Notes on Erdős' conjecture

Authors: Qihe Tang, Fanchao Kong

Source: Acta Mathematica Scientia. 20:533-541

Subject Terms: additive arithmetic function, essential convergence, sums of independent random variables, Central limit and other weak theorems, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/1563767
https://www.sciencedirect.com/science/article/pii/S0252960217306641
https://www.sciencedirect.com/science/article/abs/pii/S0252960217306641#!

Some estimates in theL p metric in the central limit theorem for additive functions: Some estimates in the \(L_p\) metric in the central limit theorem for additive functions

Authors: A. Mačiulis

Source: Lithuanian Mathematical Journal. 39:58-63

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, variance of additive functions, central limit theorem, third absolute moment of additive functions, 0101 mathematics, 01 natural sciences, Strongly additive arithmetic function, standard normal distribution, convergence of the value distribution function of strongly additive functions to the normal law in the \( L^p\)-metric

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Access URL: https://zbmath.org/1465833
https://doi.org/10.1007/bf02465536
https://link.springer.com/article/10.1007/BF02465536
https://link.springer.com/content/pdf/10.1007/BF02465536.pdf

A Note on the Convergence of Sums of Independent Random Variables

Authors: Hildebrand, Adolf

Source: The Annals of Probability, 1992 Jul 01. 20(3), 1204-1212.

Access URL: https://www.jstor.org/stable/2244639

On the Three Series Theorem in Number Theory

Authors: de la Cal, Jesus

Source: The Annals of Probability, 1989 Jan 01. 17(1), 357-361.

Access URL: https://www.jstor.org/stable/2244216

The local behaviour of some additive functions

Authors: Gediminas Stepanauskas

Source: Acta Mathematica Hungarica. 62:363-371

Subject Terms: additive arithmetic function, asymptotic formula, Arithmetic functions in probabilistic number theory, 0103 physical sciences, distribution, Asymptotic results on arithmetic functions, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/575891
https://doi.org/10.1007/bf01874656
https://link.springer.com/article/10.1007/BF01874656

The Probability Theory of Additive Arithmetic Functions

Authors: Billingsley, Patrick

Source: The Annals of Probability, 1974 Oct 01. 2(5), 749-791.

Access URL: https://www.jstor.org/stable/2959305

Nonuniform estimates of the distribution of additive arithmetical functions

Authors: V. Vilimas, G. Bareikis

Source: Lithuanian Mathematical Journal. 31:401-408

Subject Terms: additive arithmetic function, Arithmetic functions in probabilistic number theory, asymptotic estimate for the frequencies, distribution functions, Asymptotic results on arithmetic functions

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/BF00970787
https://link.springer.com/content/pdf/10.1007/BF00970787.pdf

Additive functions on shifted primes

Authors: P. D. T. A. Elliott

Source: Bulletin of the American Mathematical Society. 27:273-278

Subject Terms: additive arithmetic function, Mathematics - Number Theory, limit distribution, 01 natural sciences, Distribution functions associated with additive and positive multiplicative functions, Other results on the distribution of values or the characterization of arithmetic functions, Arithmetic functions in probabilistic number theory, concentration functions, FOS: Mathematics, shifted primes, Asymptotic results on arithmetic functions, Number Theory (math.NT), 0101 mathematics, Sums over primes

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Access URL: https://www.ams.org/bull/1992-27-02/S0273-0979-1992-00317-8/S0273-0979-1992-00317-8.pdf
http://arxiv.org/abs/math/9210214
http://ui.adsabs.harvard.edu/abs/1992math.....10214E/abstract
https://www.ams.org/bull/1992-27-02/S0273-0979-1992-00317-8/S0273-0979-1992-00317-8.pdf
https://www.ams.org/journals/bull/1992-27-02/S0273-0979-1992-00317-8/home.html

Poisson Distribution for a Sum of Additive Functions

Authors: Šiaulys, Jonas, Stepanauskas, Gediminas

Source: Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications. July 2007 97(1-3):269-279

Local limit distribution laws for a class of arithmetic functions

Authors: R. Skrabutėnas

Source: Lithuanian Mathematical Journal. 18:126-137

Subject Terms: Arithmetic functions in probabilistic number theory, real additive arithmetic function, Asymptotic results on arithmetic functions, 0101 mathematics, 01 natural sciences, local limit distribution laws, asymptotic result

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Access URL: https://link.springer.com/content/pdf/10.1007/BF00970689.pdf
https://link.springer.com/article/10.1007/BF00970689