Search Results - Distribution functions associated with additive and positive multiplicative functions

Weighted Erdős–Kac theorems via computing moments: Weighted Erdős-Kac theorems via computing moments

Authors: Fan, Kai (Steve)

Source: Acta Arithmetica. 217:99-158

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Erdős-Kac theorem, Arithmetic functions in probabilistic number theory, method of moments, Gaussian distribution, FOS: Mathematics, Asymptotic results on arithmetic functions, Number Theory (math.NT), mean values of multiplicative functions, 11K65, 11N60, 11N37

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Access URL: https://zbmath.org/7981259
https://doi.org/10.4064/aa231014-9-8

A variant of Kátai's minimax theorem for additive functions

Authors: Van Rossum-Wijsmuller, Marijke

Source: Publicationes Mathematicae Debrecen. 34:323-326

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, largest gap, sequence of positive density, asymptotic distribution, 0101 mathematics, 01 natural sciences, strongly additive function

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Access URL: https://zbmath.org/4059523

The joint distribution of q-additive functions: The joint distribution of \(q\)-additive functions

Authors: Michael Drmota

Source: Acta Arithmetica. 100:17-39

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, normal distribution, Arithmetic functions in probabilistic number theory, \(q\)-additive function, polynomial sequence, mean value, sum-of-digits function, distribution function, 0101 mathematics, Radix representation, digital problems, 01 natural sciences

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/83506?download.pdf
https://www.impan.pl/shop/publication/transaction/download/product/83506?download.pdf
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa100-1-2
https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all/100/1/83506/the-joint-distribution-of-q-additive-functions
https://ui.adsabs.harvard.edu/abs/2001AcAri.100...17D/abstract

Value distribution of g-additive functions: Value distribution of \(g\)-additive functions

Authors: Peter, Manfred Spilker, Jürgen

Source: manuscripta mathematica. 105:519-536

Subject Terms: uniform distribution, application of Halász' theorem, integer-valued arithmetical functions, uniformly almost periodic arithmetical functions, limit distribution, analogue of the Turán-Kubilius inequality, 01 natural sciences, Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, 0103 physical sciences, \(g\)-additive arithmetical function, application of Delange's theorem, Distribution of integers in special residue classes, existence of mean-values, 0101 mathematics, continuous limit distribution modulo \(m\)

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Access URL: https://link.springer.com/content/pdf/10.1007%2Fs002290100194.pdf
https://documat.unirioja.es/servlet/articulo?codigo=2804670
https://link.springer.com/article/10.1007%2Fs002290100194
https://dialnet.unirioja.es/servlet/articulo?codigo=2804670

Distribution of additive and $q$-additive functions under some conditions. II: Distribution of additive and \(q\)-additive functions under some conditions

Authors: Kátai, I. Subbarao, M. V.

Source: Publicationes Mathematicae Debrecen. 73:59-88

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, limit distribution, 0211 other engineering and technologies, \(q\)-additive functions, 02 engineering and technology, 0101 mathematics, additive functions, special conditions, 01 natural sciences

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Access URL: https://zbmath.org/2099949

On the Support of Distributions of Integer-Valued Additive Functions: On the support of distributions of integer-valued additive functions

Authors: Jonas Šiaulys

Source: Lithuanian Mathematical Journal. 44:209-218

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, support, 0101 mathematics, additive functions, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1023%2FB%3ALIMA.0000033785.30925.ea

Research problems in number theory

Authors: Kátai, I.

Source: Publicationes Mathematicae Debrecen. 24:263-276

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Other results on the distribution of values or the characterization of arithmetic functions, characterization of additive functions, Arithmetic functions in probabilistic number theory, conjectures, local behaviour of number-theoretical functions, Research exposition (monographs, survey articles) pertaining to number theory, values of multiplicative functions on special sequences, distribution of additive functions, additive representation of natural numbers, 0101 mathematics, iteration of multiplicative functions, 01 natural sciences

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Distribution of the values ofq-additive functions on polynomial sequences: Distribution of the values of \(q\)-additive functions on polynomial sequences

Authors: Imre Kátai N. L. Bassily

Source: Acta Mathematica Hungarica. 68:353-361

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, normal distribution function, Arithmetic functions in probabilistic number theory, \(q\)-additive function, 0102 computer and information sciences, 0101 mathematics, frequencies, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1007%2FBF01874349
https://link.springer.com/10.1007/BF01874349

On the limits for distributions of additive functions

Authors: Mačiulis, Algirdas Šiaulys, Jonas

Source: Lietuvos Matematikos Rinkinys, Vol 40, Iss spec. (2000)
Lietuvos matematikos rinkinys, 2000, t. 40, spec. Nr, p. 49-54.

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, characteristic function, Arithmetic functions in probabilistic number theory, additive function, QA1-939, Central limit and other weak theorems, weak convergence of distribution functions, Mathematics

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Access URL: https://zbmath.org/1880255
https://doaj.org/article/6a2ab240cbe04d5884a120de10ea15f3
https://repository.vu.lt/VU:ELABAPDB3216225&prefLang=en_US

On the distribution of translates of additive functions

Authors: Imre Kátai Karl-Heinz Indlekofer

Source: Acta Mathematica Hungarica. 61:343-356

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, centering, Arithmetic functions in probabilistic number theory, 0103 physical sciences, 0101 mathematics, additive functions, limiting distribution, 01 natural sciences

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Access URL: https://zbmath.org/508724
https://doi.org/10.1007/bf01874690
https://link.springer.com/article/10.1007/BF01874690

The continuity of the limiting distribution of a function of two additive functions

Authors: Galambos, Janos Kátai, Imre

Source: Mathematische Zeitschrift. 204:247-252

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, 510.mathematics, Arithmetic functions in probabilistic number theory, continuous limiting distribution, 0101 mathematics, additive arithmetical functions, 01 natural sciences, Article

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Access URL: https://zbmath.org/4105072
https://doi.org/10.1007/bf02570871
https://link.springer.com/article/10.1007%2FBF02570871

The mean values of multiplicative functions. II: The mean values of multiplicative functions. I

Authors: Gediminas Stepanauskas

Source: Lithuanian Mathematical Journal. 37:162-170

Subject Terms: asymptotic uniform distribution modulo 1, distribution functions, sums of multiplicative functions, additive functions, 01 natural sciences, mean values of multiplicative functions, Other results on the distribution of values or the characterization of arithmetic functions, Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, multiplicative functions, distribution, mean values, mean value, Rate of growth of arithmetic functions, Asymptotic results on arithmetic functions, 0101 mathematics

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Access URL: https://zbmath.org/1446753
https://zbmath.org/1261180
https://link.springer.com/article/10.1007/BF02465889

An Erdős-Kac theorem for systems of q-additive functions: An Erdős-Kac theorem for systems of \(q\)-additive functions

Authors: Robert F. Tichy Jörg M. Thuswaldner

Source: Indagationes Mathematicae. 11:283-291

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Mathematics(all), Arithmetic functions in probabilistic number theory, Limit theorems in probability theory, limiting laws, \(q\)-additive functions, Distribution of integers in special residue classes, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/1611987
https://doi.org/10.1016/s0019-3577(00)89084-9
https://graz.pure.elsevier.com/en/publications/an-erdös-kac-theorem-for-systems-of-q-additive-functions
https://www.sciencedirect.com/science/article/pii/S0019357700890849
https://www.sciencedirect.com/science/article/abs/pii/S0019357700890849

The Limit Distribution of a Number Theoretic Function Arising from a Problem in Statistical Mechanics: The limit distribution of a number theoretic function arising from a problem in statistical mechanics

Authors: Peter, Manfred

Source: Journal of Number Theory. 90:265-280

Subject Terms: Algebra and Number Theory, nonexistence of a limit, limit distribution, absolutely continuous limit distribution, Miscellaneous applications of number theory, Farey fractions, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, 01 natural sciences, Distribution functions associated with additive and positive multiplicative functions, arithmetical function, 0103 physical sciences, almost periodic functions, 0101 mathematics, spin chain, class numbers

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Access URL: https://core.ac.uk/display/82025891
https://www.sciencedirect.com/science/article/pii/S0022314X01926666
https://www.sciencedirect.com/science/article/abs/pii/S0022314X01926666

Multiplicative functions with difference tending to zero

Authors: Don Zagier Eduard Wirsing

Source: Acta Arithmetica. 100:75-78

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, multiplicative functions, Arithmetic functions, related numbers, inversion formulas, 0101 mathematics, additive functions, 01 natural sciences

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/83510?download.pdf
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https://core.ac.uk/display/41496963
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/100/1/83510/multiplicative-functions-with-difference-tending-to-zero
https://eudml.org/doc/277863
https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_3125296
https://ui.adsabs.harvard.edu/abs/2001AcAri.100...75W/abstract

Sums of nonnegative multiplicative functions over integers without large prime factors I: Sums of nonnegative multiplicative functions over integers without large prime factors. II

Authors: Joung Min Song

Source: Acta Arithmetica. 97:329-351

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, multiplicative functions, integers with no large prime factor, weighted sums, multiplicative function, Asymptotic results on arithmetic functions, 0101 mathematics, integers with no large prime divisor, Distribution of integers with specified multiplicative constraints, 01 natural sciences

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/82277?download.pdf
https://zbmath.org/1721460
https://doi.org/10.4064/aa102-2-1
https://zbmath.org/1605202
https://doi.org/10.4064/aa97-4-3
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/97/4/83322/sums-of-nonnegative-multiplicative-functions-over-integers-without-large-prime-factors-i
http://ui.adsabs.harvard.edu/abs/2001AcAri..97..329S/abstract
http://journals.impan.pl/cgi-bin/doi?aa97-4-3
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/102/2/82277/sums-of-nonnegative-multiplicative-functions-over-integers-without-large-prime-factors-ii
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa102-2-1

The Concentration Function of Additive Functions with Special Weight: The concentration function of additive functions with special weight

Authors: N. M. Timofeev M. B. Khripunova

Source: Mathematical Notes. 76:244-263

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, prime divisor, concentration function of additive functions, Dirichlet character, coprime integers, Ruzsa inequality, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2121463
https://doi.org/10.1023/b:matn.0000036762.34709.45
https://link.springer.com/article/10.1023/B%3AMATN.0000036762.34709.45
https://link.springer.com/content/pdf/10.1023/B:MATN.0000036762.34709.45.pdf

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

Decay of Mean Values of Multiplicative Functions: Decay of mean values of multiplicative functions

Authors: Kannan Soundararajan Andrew Granville

Source: Canadian Journal of Mathematics. 55:1191-1230

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, integral equations, Mathematics - Number Theory, explicit upper bounds, FOS: Mathematics, Rate of growth of arithmetic functions, Asymptotic results on arithmetic functions, Number Theory (math.NT), 0101 mathematics, mean value of multiplicative functions, 01 natural sciences

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Access URL: http://arxiv.org/pdf/math/9911246
http://arxiv.org/abs/math/9911246
https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/decay-of-mean-values-of-multiplicative-functions/9BE47DD2587F7A1078B1D9219B5B3F82
https://dialnet.unirioja.es/servlet/articulo?codigo=777073

A Non-Uniform Estimate in the Central Limit Theorem for Sequences of Strongly Additive Functions: A non-uniform estimate in the central limit theorem for sequences of strongly additive functions

Authors: A. Maĉiulis

Source: The Ramanujan Journal. 3:389-404

Subject Terms: normal distribution, Elliott-Timofeev theorem, central limit theorem, Central limit and other weak theorems, real-valued strongly additive function, remainder term estimates, 01 natural sciences, value distribution of additive arithmetic functions, convergence of distribution functions, Distribution functions associated with additive and positive multiplicative functions, Arithmetic functions in probabilistic number theory, Esseen's inequality, Asymptotic results on arithmetic functions, 0101 mathematics

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Access URL: https://link.springer.com/article/10.1023/A:1009857207237