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

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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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

Multivariate normal distribution for integral points on varieties

Authors: El-Baz, D., Loughran, D., Sofos, E.

Source: El-Baz, D, Loughran, D & Sofos, E 2022, 'Multivariate normal distribution for integral points on varieties', Transactions of the American Mathematical Society, vol. 375, no. 5, pp. 3089-3128. https://doi.org/10.1090/tran/8545
Transactions of the American Mathematical Society

Subject Terms: Erdős-Kac theorem, Mathematics - Number Theory, sieve, Probability (math.PR), name=General Mathematics, name=Applied Mathematics, Central limit and other weak theorems, distribution of additive functions, 01 natural sciences, Distribution functions associated with additive and positive multiplicative functions, primes, Primes represented by polynomials, other multiplicative structures of polynomial values, Mathematics - Algebraic Geometry, Arithmetic functions in probabilistic number theory, varieties, FOS: Mathematics, Applications of sieve methods, Rational points, Number Theory (math.NT), 0101 mathematics, Varieties over global fields, Algebraic Geometry (math.AG), Mathematics - Probability

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Access URL: https://www.ams.org/tran/0000-000-00/S0002-9947-2022-08545-7/S0002-9947-2022-08545-7.pdf
http://arxiv.org/abs/2001.10970
https://purehost.bath.ac.uk/ws/files/222268437/EKM_final.pdf
http://hdl.handle.net/21.11116/0000-000A-2223-8
http://hdl.handle.net/21.11116/0000-000A-2225-6
http://hdl.handle.net/21.11116/0000-000A-3DAF-E

On a Distribution Property of the Residual Order of a (mod p)— IV: On a distribution property of the residual order of \(a\pmod p\). II

Authors: CHINEN, Koji, MURATA, Leo

Source: Developments in Mathematics ISBN: 0387304142
Proc. Japan Acad. Ser. A Math. Sci. 79, no. 2 (2003), 28-32
J. Math. Soc. Japan 58, no. 3 (2006), 693-720

Subject Terms: arithmetic progression, residual order, natural density, 11A07, 11R18, 02 engineering and technology, 01 natural sciences, The residual order, Distribution functions associated with additive and positive multiplicative functions, Density theorems, distribution, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Artin's conjecture (for primitive roots), Asymptotic results on arithmetic functions, 11N05, 11N25, 11R18, order, Number Theory (math.NT), 0101 mathematics, Artin's conjecture, Distribution of integers with specified multiplicative constraints, density, residual index, Algebra and Number Theory, Residual order, residue classes, Mathematics - Number Theory, The Artin's conjecture, Distribution of primitive roots, Artin's conjecture for primitive roots, 11N25, 11N05, The Artin's conjecture for primitive roots, Distribution of primes, Cyclotomic extensions, Artin's primitive root conjecture, Distribution of integers in special residue classes

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Access URL: http://arxiv.org/abs/math/0211083
http://arxiv.org/abs/math/0211077
https://zbmath.org/2082496
https://doi.org/10.1016/j.jnt.2003.06.007
https://zbmath.org/2024715
https://doi.org/10.3792/pjaa.79.28
https://zbmath.org/2082495
https://doi.org/10.1016/j.jnt.2003.06.005
https://projecteuclid.org/journals/proceedings-of-the-japan-academy-series-a-mathematical-sciences/volume-80/issue-9/On-a-distribution-property-of-the-residual-order-of-a/10.3792/pjaa.80.182.full
https://rd.springer.com/chapter/10.1007/0-387-30829-6_2
https://ci.nii.ac.jp/naid/40005723985
https://projecteuclid.org/download/pdf_1/euclid.pja/1116442487
https://arxiv.org/pdf/math/0211077
https://ui.adsabs.harvard.edu/abs/2002math.....11083M/abstract
https://projecteuclid.org/download/pdf_1/euclid.jmsj/1156342034
https://ci.nii.ac.jp/naid/10018381051
https://projecteuclid.org/journals/journal-of-the-mathematical-society-of-japan/volume-58/issue-3/On-a-distribution-property-of-the-residual-order-of-a/10.2969/jmsj/1156342034.full
https://www.sciencedirect.com/science/article/abs/pii/S0022314X03001525
https://www.sciencedirect.com/science/article/pii/S0022314X03001525
https://core.ac.uk/display/82447320
http://projecteuclid.org/euclid.pja/1116443604
http://projecteuclid.org/euclid.jmsj/1156342034

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

Composite positive integers with an average prime factor

Authors: LUCA F, PAPPALARDI, FRANCESCO

Source: Acta Arithmetica. 129:197-201

Subject Terms: Asymptotic results on arithmetic functions, Distribution functions associated with additive and positive multiplicative functions, Goldbach-type theorems, other additive questions involving primes, 0101 mathematics, 01 natural sciences

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/82127?download.pdf
http://journals.impan.pl/cgi-bin/doi?aa129-2-5
https://core.ac.uk/display/53893196
https://ui.adsabs.harvard.edu/abs/2007AcAri.129..197L/abstract
https://eudml.org/doc/278014
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/129/2/82127/composite-positive-integers-with-an-average-prime-factor
https://iris.uniroma3.it/handle/11590/141649
http://journals.impan.gov.pl/aa/Inf/129-2-5.html
https://doi.org/10.4064/aa129-2-5
https://hdl.handle.net/11590/141649

Sums of the additive divisor problem type and the inner product method

Authors: M. Jutila

Source: Journal of Mathematical Sciences. 137:4755-4761

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, divisor function, Multiplicative number theory, spectral summation formula, Fourier coefficients, Asymptotic results on arithmetic functions, 0101 mathematics, 01 natural sciences, Maass form

File Description: application/xml

Access URL: https://link.springer.com/article/10.1007/s10958-006-0271-y

PRIME DIVISORS OF LUCAS SEQUENCES AND A CONJECTURE OF SKAŁBA: Prime divisors of Lucas sequences and a conjecture of Skałba

Authors: Florian Luca, Pantelimon Stănică

Source: International Journal of Number Theory. :583-591

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Lucas sequences, prime numbers, Fibonacci and Lucas numbers and polynomials and generalizations, Asymptotic results on arithmetic functions, divisibility, 0101 mathematics, 01 natural sciences

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Access URL: http://faculty.nps.edu/pstanica/research/onskalba.pdf
https://zbmath.org/2244191
https://doi.org/10.1142/s1793042105000285
https://www.worldscientific.com/doi/abs/10.1142/S1793042105000285
https://faculty.nps.edu/pstanica/research/onskalba.pdf

The Sum-of-Digits Function of Squares: The sum-of-digits function of squares

Authors: Drmota, Michael, Rivat, Joel

Contributors: Rivat, Joel

Source: Journal of the London Mathematical Society. 72:273-292

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, digital sums, sum-of-digits function, 0102 computer and information sciences, 0101 mathematics, Radix representation, digital problems, 01 natural sciences, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/xml

Access URL: http://dmg.tuwien.ac.at/drmota/nsquare4.pdf
https://zbmath.org/2228485
https://doi.org/10.1112/s0024610705006769
http://www.dmg.tuwien.ac.at/drmota/nsquare4.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=2207563
http://doi.wiley.com/10.1112/S0024610705006769
https://www.dmg.tuwien.ac.at/drmota/nsquare4.pdf
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024610705006769
https://hal.archives-ouvertes.fr/hal-02529975

Moments of the probability density functions of error terms in divisor problems

Authors: Lau, YK, Tsang, KM

Source: Proceedings of the American Mathematical Society. 133:1283-1290

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, 0103 physical sciences, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://www.ams.org/proc/2005-133-05/S0002-9939-04-07825-6/S0002-9939-04-07825-6.pdf
https://zbmath.org/2140111
https://doi.org/10.1090/s0002-9939-04-07825-6
https://www.ams.org/journals/proc/2005-133-05/S0002-9939-04-07825-6/home.html
https://www.jstor.org/stable/4097778
https://www.ams.org/proc/2005-133-05/S0002-9939-04-07825-6/S0002-9939-04-07825-6.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=1168662
https://hub.hku.hk/bitstream/10722/156128/1/content.pdf
http://hdl.handle.net/10722/156128

A Generalization of the Erdös-Kac Theorem and its Applications: A generalization of the Erdős-Kac theorem and its applications

Authors: Liu, Yu-Ru

Source: Canadian Mathematical Bulletin. 47:589-606

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, asymptotic results on arithmetic functions, Erdős-Kac theorem, 13. Climate action, 11N80, Generalized primes and integers, 11N60, 0101 mathematics, 01 natural sciences, generalized primes

File Description: application/xml

Access URL: https://zbmath.org/2147189
https://doi.org/10.4153/cmb-2004-057-4
https://dialnet.unirioja.es/servlet/articulo?codigo=1035356
https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/generalization-of-the-erdoskac-theorem-and-its-applications/01697DD7C702CD0FF7239E46A9502C63

On the average number of elements in a finite field with order or index in a prescribed residue class

Authors: Moree, P.

Source: Finite Fields and Their Applications. 10:438-463

Subject Terms: Algebra and Number Theory, Mathematics - Number Theory, natural density, Applied Mathematics, 0102 computer and information sciences, 01 natural sciences, Theoretical Computer Science, Distribution functions associated with additive and positive multiplicative functions, 11N37, 11T99, Natural density, FOS: Mathematics, Order, Residue class, Asymptotic results on arithmetic functions, Distribution of integers in special residue classes, Congruences, primitive roots, residue systems, order, Number Theory (math.NT), 0101 mathematics, residue class, Engineering(all)

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Access URL: http://arxiv.org/abs/math/0212220
https://arxiv.org/pdf/math/0212220
https://arxiv.org/abs/math/0212220
https://www.narcis.nl/publication/RecordID/oai%3Adare.uva.nl%3Apublications%2Fef1e38fc-b67b-4c12-a1af-ce7a05507d5b
https://www.sciencedirect.com/science/article/abs/pii/S1071579703000856
https://ui.adsabs.harvard.edu/abs/2002math.....12220M/abstract
https://www.sciencedirect.com/science/article/pii/S1071579703000856
https://core.ac.uk/display/85888963

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

File Description: application/xml

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

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

File Description: application/xml

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

The number of unsieved integers up to x: The number of unsieved integers up to~\(x\)

Authors: Andrew Granville, Kannan Soundararajan

Source: Acta Arithmetica. 115:305-328

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, integral equation, multiplicative functions, mean value range for a class of functions, Mathematics - Number Theory, 0103 physical sciences, FOS: Mathematics, Asymptotic results on arithmetic functions, Number Theory (math.NT), 0101 mathematics, 01 natural sciences, Sieves, Lipschitz-type estimates

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/83116?download.pdf
http://arxiv.org/abs/math/0308009
http://journals.impan.pl/cgi-bin/doi?aa115-4-1
https://www.impan.pl/shop/publication/transaction/download/product/83116?download.pdf
http://ui.adsabs.harvard.edu/abs/2004AcAri.115..305G/abstract
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa115-4-1
https://core.ac.uk/display/79530230
https://arxiv.org/pdf/math/0308009.pdf
https://arxiv.org/abs/math/0308009

The Erdős Theorem and the Halberstam Theorem in function fields: The Erdős theorem and the Halberstam theorem in function fields

Authors: Liu, Yu-Ru

Source: Acta Arithmetica. 114:323-330

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, Erdős-Kac theorem, Arithmetic theory of algebraic function fields, mean irreducible polynomials, 0101 mathematics, analogue of the normal order of \(\omega(p-1)\), 01 natural sciences, polynomial ring over a finite field

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/82512?download.pdf
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa114-4-3
https://ui.adsabs.harvard.edu/abs/2004AcAri.114..323L/abstract
https://www.impan.pl/shop/publication/transaction/download/product/82512?download.pdf
http://journals.impan.pl/cgi-bin/doi?aa114-4-3

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

File Description: application/xml

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

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

File Description: application/xml

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

Arithmetic Processes in Semigroups: Arithmetic processes in semigroups

Authors: K.-H. Indlekofer, Gintautas Bareikis

Source: Lithuanian Mathematical Journal. 43:347-366

Subject Terms: Distribution functions associated with additive and positive multiplicative functions, degree mapping, Arithmetic functions in probabilistic number theory, multiplicative function, Measures on groups and semigroups, etc, polynomials over a finite field, Probability theory on algebraic and topological structures, arithmetic semigroup, 0101 mathematics, process with independent increments, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2108220
https://doi.org/10.1023/b:lima.0000009684.86450.ac
https://link.springer.com/article/10.1023/B%3ALIMA.0000009684.86450.ac