Averages of multiplicative functions along equidistributed sequences

Authors: Stephanie Chan, Peter Koymans, Carlo Pagano, Efthymios Sofos

Source: arXiv
Journal of Number Theory, 273

Subject Terms: multiplicative functions, Mathematics - Number Theory, Sieve theory, Arithmetic functions, related numbers, inversion formulas, FOS: Mathematics, Asymptotic results on arithmetic functions, Rate of growth of arithmetic functions, Number Theory (math.NT), sieve theory, Multiplicative functions

File Description: application/xml; application/application/pdf

Access URL: http://arxiv.org/abs/2402.08710
https://zbmath.org/7995932
https://doi.org/10.1016/j.jnt.2025.01.005
http://hdl.handle.net/20.500.11850/684644
http://hdl.handle.net/20.500.11850/728168

Distribution of square free integers involving the floor function

Authors: Hu, Jiayuan, Wu, Jie^{Aff2, IDs10998025006875_cor1}

Source: Periodica Mathematica Hungarica. :1-9

Refined asymptotic expansions of Dirichlet, Euler and Mertens type

Authors: Popa, Dumitru^{Aff1, IDs13226025008685_cor1}

Source: Indian Journal of Pure and Applied Mathematics: Published by the Indian National Science Academy. :1-18

Mean value theorems in multiplicative systems and joint ergodicity of additive and multiplicative actions

Authors: Charamaras, Dimitrios

Source: Transactions of the American Mathematical Society. 378:1883-1937

Subject Terms: Relations between ergodic theory and number theory, Arithmetic combinatorics, higher degree uniformity, multiplicative structures of the integers, Ergodic theorems, spectral theory, Markov operators, multiplicative systems, Mathematics - Number Theory, Primary: 37A44, Secondary: 11N37, 11B30, additive ergodic average, FOS: Mathematics, Asymptotic results on arithmetic functions, Dynamical Systems (math.DS), Number Theory (math.NT), Mathematics - Dynamical Systems

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Access URL: http://arxiv.org/abs/2403.13744
https://zbmath.org/8004993
https://doi.org/10.1090/tran/9321

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

Average behaviour of Fourier coefficients of $$j$$-symmetric power $$L$$-functions over some polynomials: Average behaviour of Fourier coefficients of \(j\)-symmetric power \(L\)-functions over some polynomials

Authors: Sarkar, A., Shahvez Alam, M.

Source: Acta Mathematica Hungarica. 174:75-93

Subject Terms: Fourier coefficients of automorphic forms, symmetric power \(L\) function, Fourier coefficients of cusp form, \(\zeta (s)\) and \(L(s, \chi)\), asymptotic behaviour, Asymptotic results on arithmetic functions, Holomorphic modular forms of integral weight

File Description: application/xml

Access URL: https://zbmath.org/7966618
https://doi.org/10.1007/s10474-024-01467-2

Some remarks on the [x/n]-sequence: Some remarks on the \([x/n]\)-sequence

Authors: Kota Saito, Yuta Suzuki, Wataru Takeda, Yuuya Yoshida

Source: Research in Number Theory. 11

Subject Terms: exponent pair, Primary: 11N37. Secondary: 11N25, 11N69, 11L03, 11L07, Number Theory, integral part, FOS: Mathematics, Asymptotic results on arithmetic functions, Distribution of integers in special residue classes, Number Theory (math.NT), Estimates on exponential sums, arithmetic functions, Trigonometric and exponential sums (general theory), Distribution of integers with specified multiplicative constraints, exponential sums

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Access URL: http://arxiv.org/abs/2312.15642
https://zbmath.org/8034693
https://doi.org/10.1007/s40993-025-00632-y

The shifted prime-divisor function over shifted primes

Authors: Fan, S.

Source: arXiv

Subject Terms: sieve methods, Mathematics - Number Theory, shifted-prime divisors, Density, gaps, topology, FOS: Mathematics, Applications of sieve methods, moments, Asymptotic results on arithmetic functions, Primary: 11N36, 11N37, Secondary: 11B05, Number Theory (math.NT), mean values of multiplicative functions

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2406.05217
http://hdl.handle.net/21.11116/0000-000F-8300-C
http://hdl.handle.net/21.11116/0000-000F-8302-A

Visibility Properties Of Lattice Points In Multiple Random Walks: Visibility properties of lattice points in multiple random walks

Authors: Lu, M.

Source: Acta Mathematica Hungarica. 172:289-305

Subject Terms: random walk, Strong limit theorems, Sums of independent random variables, random walks, Lattices and convex bodies (number-theoretic aspects), multiplicative function, Asymptotic results on arithmetic functions, visible lattice point

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Access URL: https://zbmath.org/7857899
https://doi.org/10.1007/s10474-024-01412-3

The Selberg–Delange method and mean value of arithmetic functions over short intervals

Authors: Kaur, Amrinder ^⁎, Sankaranarayanan, Ayyadurai

Source: In Journal of Number Theory February 2024 255:37-61

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

A minimax theorem for additive functions

Authors: Kátai, I.

Source: Publicationes Mathematicae Debrecen. 30:249-252

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

File Description: application/xml

Access URL: https://zbmath.org/3855232

Additive functions vanishing outside a given set of primes. Part I. Limiting distribution on short intervals: Additive functions vanishing outside a given set of primes. I: Limiting distribution on short intervals

Authors: Galambos, János, Indlekofer, Karl-Heinz

Source: Publicationes Mathematicae Debrecen. 40:211-217

Subject Terms: Arithmetic functions in probabilistic number theory, Erdős-Wintner type criterion, short intervals, Asymptotic results on arithmetic functions, 0101 mathematics, limiting distribution, 01 natural sciences, strongly additive function

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Access URL: https://zbmath.org/40447

Arithmetical expressions and asymptotic formulae for generalized totient functions

Authors: Haukkanen, Pentti

Source: Publicationes Mathematicae Debrecen. 40:35-42

Subject Terms: Euler's totient function, totient functions, multiplicative functions, Dedekind's function, Arithmetic functions, related numbers, inversion formulas, Asymptotic results on arithmetic functions, summatory functions, 0101 mathematics, asymptotic formulas, 01 natural sciences

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Access URL: https://zbmath.org/55008

Problems and results on consecutive integers

Authors: Erdős, Paul

Source: Publicationes Mathematicae Debrecen. 23:271-282

Subject Terms: Distribution of primes, Problem books, Research exposition (monographs, survey articles) pertaining to number theory, Asymptotic results on arithmetic functions, 0101 mathematics, 01 natural sciences, Primes

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Access URL: https://zbmath.org/3549076

Divisibility properties of arithmetical functions

Authors: Katai, I.

Source: Publicationes Mathematicae Debrecen. 26:55-63

Subject Terms: Arithmetic functions in probabilistic number theory, multiplicative functions, Special sequences and polynomials, distribution of values, Asymptotic results on arithmetic functions, 0101 mathematics, additive functions, 01 natural sciences, divisibility properties

File Description: application/xml

Access URL: https://zbmath.org/3674192
https://zbmath.org/3661438

On a class of arithmetical functions

Authors: Grytczuk, Aleksander

Source: Publicationes Mathematicae Debrecen. 32:195-202

Subject Terms: asymptotic formula, sums of arithmetical functions, Asymptotic results on arithmetic functions, Dirichlet series, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3979174

Bemerkungen zu einem Teilerproblem

Authors: Schierwagen, A.

Source: Publicationes Mathematicae Debrecen. 25:41-46

Subject Terms: Asymptotic Result, Riemann Zeta- Function, Asymptotic results on arithmetic functions, 0101 mathematics, Divisor Function, 01 natural sciences, Divisor Problem

File Description: application/xml

Access URL: https://zbmath.org/3608138

On a problem of Evelyn--Linfoot and Page in additive number theory: On a problem of Evelyn-Linfoot and Page in additive number theory

Authors: Pomerance, Carl, Suryanarayana, D.

Source: Publicationes Mathematicae Debrecen. 26:237-244

Subject Terms: k-free integers, Additive number theory, partitions, Distribution of primes, Primes in congruence classes, Asymptotic results on arithmetic functions, 0101 mathematics, 01 natural sciences, number of representations

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Access URL: https://zbmath.org/3523687

The density of a sequence defined in terms of additive functions

Authors: Galambos, Janos

Source: Publicationes Mathematicae Debrecen. 23:263-266

Subject Terms: Arithmetic functions in probabilistic number theory, Special sequences and polynomials, Asymptotic results on arithmetic functions, 0101 mathematics, Goldbach-type theorems, other additive questions involving primes, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3549083