Complex Valued Multiplicative Functions with Bounded Partial Sums

Authors: Aymone, Marco^{Aff1, IDs00574022003068_cor1}

Source: Bulletin of the Brazilian Mathematical Society, New Series: Boletim da Sociedade Brasileira de Matemática. 53(4):1317-1329

Fonctions multiplicatives, sommes d’exponentielles, et loi des grands nombres

Authors: Tenenbaum, Gérald

Source: In Indagationes Mathematicae March 2016 27(2):590-600

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

SUMS OF MULTIPLICATIVE FUNCTIONS OVER A BEATTY SEQUENCE

Authors: Güloǧlu, A.M., Wesley Nevans, C.

Source: Bulletin of the Australian Mathematical Society

Subject Terms: Sums of multiplicative functions, Beatty sequences, 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/F83D838ECBFECD39AFD91172D1469AB5/S0004972708000853a.pdf/div-class-title-sums-of-multiplicative-functions-over-a-beatty-sequence-div.pdf
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0004972708000853
http://repository.bilkent.edu.tr/handle/11693/23001
https://ui.adsabs.harvard.edu/abs/2008arXiv0801.2796G/abstract
https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/sums-of-multiplicative-functions-over-a-beatty-sequence/F83D838ECBFECD39AFD91172D1469AB5
https://hdl.handle.net/11693/23001

The multiplicative group of rationals generated by the shifted primes, I: The multiplicative group of rationals generated by the shifted primes. I

Authors: Elliott, P.D.T.A.

Source: Journal für die reine und angewandte Mathematik (Crelles Journal). 1995:169-216

Subject Terms: Primes in congruence classes, Representation problems, Harmonic analysis and almost periodicity in probabilistic number theory, 01 natural sciences, Article, estimates for sums of multiplicative functions on shifted primes, dispersion method, 510.mathematics, Arithmetic functions in probabilistic number theory, Selberg sieve, harmonic analysis, Applications of sieve methods, Asymptotic results on arithmetic functions, distribution of primes in residue classes to large moduli, 0101 mathematics, multiplicative group of positive rationals, large sieve

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Access URL: https://zbmath.org/768181
https://doi.org/10.1515/crll.1995.463.169
https://zbmath.org/1414387
https://doi.org/10.1515/crll.2000.017
https://www.degruyter.com/view/j/crll.2000.2000.issue-519/crll.2000.017/crll.2000.017.pdf

The bound of sums of multiplicative functions with shifted arguments

Authors: N. M. Timofeev

Source: Mathematical Notes. 54:1138-1146

Subject Terms: Gallagher's inequality, sums of multiplicative functions of absolute value 1 with shifted arguments, estimates of exponential sums, Asymptotic results on arithmetic functions, Liouville function, application of Selberg's sieve, 0101 mathematics, Bombieri-type estimates for multiplicative functions, 01 natural sciences

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Access URL: https://zbmath.org/795603
https://doi.org/10.1007/bf01208394
https://link.springer.com/article/10.1007/BF01208394

Multiplicative Functions on Arithmetic Progressions: V. Composite Moduli: Multiplicative functions on arithmetic progressions. V: Composite moduli

Authors: P. D. T. A. Elliott

Source: Journal of the London Mathematical Society. :408-424

Subject Terms: composite moduli, Dirichlet divisor function, sums of multiplicative functions, primitive character, 01 natural sciences, Estimates on character sums, Other results on the distribution of values or the characterization of arithmetic functions, analogues of Bombieri-Vinogradov theorem, Applications of sieve methods, Asymptotic results on arithmetic functions, multiplicative functions on arithmetic progressions, asymptotic behavior, 0101 mathematics, Sums over primes

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Access URL: https://zbmath.org/4097501
https://doi.org/10.1112/jlms/s2-41.3.408
https://academic.oup.com/jlms/article-pdf/s2-41/3/408/3036205/s2-41-3-408.pdf

Multiplicative functions on arithmetic progressions

Authors: P. D. T. A. Elliott

Source: Mathematika. 34:199-206

Subject Terms: well- distributed, Primes in congruence classes, distribution on arithmetic progressions, multiplicative function, Halász' method, Asymptotic results on arithmetic functions, sums of multiplicative functions, generating Dirichlet series, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/4037935
https://doi.org/10.1112/s0025579300013450
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0025579300013450
https://www.cambridge.org/core/journals/mathematika/article/multiplicative-functions-on-arithmetic-progressions/FCEACC99B5D44E79E882AE9096191DBA

Distribution of additive functions on arithmetic progressions

Authors: G. Styapanauskas

Source: Lithuanian Mathematical Journal. 19:552-561

Subject Terms: arithmetic progressions, Arithmetic functions in probabilistic number theory, Primes in congruence classes, error estimates, Asymptotic results on arithmetic functions, distribution of additive functions, normal law, sums of multiplicative functions, 0101 mathematics, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1007/BF00970730

Sums of multiplicative functions and limit theorems in probabilistic number theory. I: Sums of multiplicative functions and limit theorems in probabilistic number theory. II

Authors: E. Manstavičius

Source: Lithuanian Mathematical Journal. 19:251-261

Subject Terms: limiting distribution theorem, limit theorems, distribution of arithmetic functions, sums of multiplicative functions, multiplicative arithmetical functions, 01 natural sciences, Distribution functions associated with additive and positive multiplicative functions, Halasz method, Arithmetic functions in probabilistic number theory, standard normal law, additive function, Halasz's method, multiplicative arithmetic function, Asymptotic results on arithmetic functions, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/3786917
https://doi.org/10.1007/bf00969613
https://zbmath.org/3670541
https://doi.org/10.1007/bf00970614
https://zbmath.org/3643378
https://link.springer.com/content/pdf/10.1007/BF00970614.pdf
https://link.springer.com/article/10.1007%2FBF00970614
https://link.springer.com/content/pdf/10.1007/BF00970614.pdf

Asymptotic results on sums of some multiplicative functions

Authors: Sita Ramaiah, V., Suryanarayana, D.

Subject Terms: k-free integers, divisor functions, asymptotic formula, number of k-free divisors, Moebius function, multiplicative arithmetical function, Asymptotic results on arithmetic functions, sums of multiplicative functions, divisor problem, Riemann hypothesis

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Access URL: https://zbmath.org/3783122
https://zbmath.org/3825936

A new method of truncating additive functions

Authors: Evlikov, V. V.

Subject Terms: Arithmetic functions in probabilistic number theory, distribution, Asymptotic results on arithmetic functions, sums of multiplicative functions, contribution of big primes, new method of truncating additive functions

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Access URL: https://zbmath.org/3771730

On a conjecture concerning sums of multiplicative functions

Authors: Tulyaganov, S. T.

Subject Terms: multiplicative functions of class \(N\), Wirsing theorem, multiplicative functions of class \(\Omega\), Asymptotic results on arithmetic functions, Rate of growth of arithmetic functions, asymptotic formulae, sums over multiplicative functions, Delange theorem, disproof of a conjecture of Levin-Fainleib

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Access URL: https://zbmath.org/30190

On an upper bound for biquadratic Weyl sums

Authors: Deshouillers, Jean-Marc

Subject Terms: estimation of sums over multiplicative functions in residue classes, Hardy-Littlewood method, Waring problem for biquadrates, Asymptotic results on arithmetic functions, Waring's problem and variants, Estimates on exponential sums, estimates of exponential sums with explicit constants

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Access URL: https://zbmath.org/165239

Asymptotic behavior of sums of multiplicative functions.

Authors: Levin, B. V., Faĭnleĭb, A. S.

Subject Terms: Asymptotic results on arithmetic functions, asymptotic behavior, sums of multiplicative functions, additive functions

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Access URL: https://zbmath.org/3342070

Comparison of sums of multiplicative functions

Authors: Tulyaganov, S. T.

Subject Terms: multiplicative functions of class \(N\), Wirsing theorem, multiplicative functions of class \(\Omega\), Asymptotic results on arithmetic functions, Rate of growth of arithmetic functions, asymptotic formulae, Delange theorem, sums over multiplicative functions

File Description: application/xml

Access URL: https://zbmath.org/30198

Extremal problems in sieve theory

Authors: Hildebrand, A.

Subject Terms: extremal problems, sieve, Applications of sieve methods, survey, sums of multiplicative functions, Sieves

File Description: application/xml

Access URL: https://zbmath.org/1181630

Mean values of multiplicative functions on shifted numbers

Authors: Stepanauskas, G.

Subject Terms: asymptotic formula, Arithmetic functions in probabilistic number theory, mean values, Asymptotic results on arithmetic functions, sums of multiplicative functions, multiplicative functions on shifted numbers

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Access URL: https://zbmath.org/1296190

Distribution of ``near primes'' in polynomial sequences

Authors: Levin, B. V.

Subject Terms: sieve methods, Applications of sieve methods, Asymptotic results on arithmetic functions, sums of multiplicative functions, retarded differential equation, Distribution of integers with specified multiplicative constraints, Goldbach-type theorems, other additive questions involving primes

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Access URL: https://zbmath.org/3275701

Asymptotic behaviour of solutions of some differential-difference equations

Authors: Chariev, U.

Subject Terms: Asymptotic theory of functional-differential equations, differential-difference equations, Asymptotic results on arithmetic functions, sums of multiplicative functions, asymptotic result

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Access URL: https://zbmath.org/3647014