Arithmetic functions on a Dedekind domain.

Authors: Phillips, Andrew¹ (AUTHOR) aphillips1@collegeofidaho.edu

Source: Communications in Algebra. Nov2025, p1-23. 23p.

Subject Terms: *ARITHMETIC functions, *COMMUTATIVE rings, *INTEGRAL domains, *POWER series

Use of simple arithmetic operations to construct efficiently implementable Boolean functions possessing high nonlinearity and good resistance to algebraic attacks.

Authors: Carlet, Claude^1,2 (AUTHOR) claude.carlet@univ-paris8.fr, Sarkar, Palash^1,3 (AUTHOR) palash@isical.ac.in

Source: Discrete Applied Mathematics. Oct2025, Vol. 373, p256-270. 15p.

Subject Terms: *ARITHMETIC functions, *COMPUTATIONAL complexity, *BOOLEAN functions, *ARITHMETIC, *INTEGERS

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

On the generalization of Roth's theorem.

Authors: Dolce, Paolo¹ dolce@westlake.edu.cn, Zucconi, Francesco² francesco.zucconi@uniud.it

Source: Kyoto Journal of Mathematics. 2025, Vol. 65 Issue 3, p503-535. 33p.

Subject Terms: *ARITHMETIC functions, *GENERALIZATION

The Chowla conjecture and Landau–Siegel zeroes.

Authors: JASKARI, MIKKO¹ (AUTHOR) mikko.m.jaskari@utu.fi, SACHPAZIS, STELIOS¹ (AUTHOR)

Source: Mathematical Proceedings of the Cambridge Philosophical Society. Jul2025, Vol. 179 Issue 1, p167-187. 21p.

Subject Terms: *NUMBER theory, *ARITHMETIC functions, *DIRICHLET series, *MATHEMATICAL bounds

Graphs with three and four distinct eigenvalues based on circulants

Authors: Bašić, Milan

Source: Linear Algebra and its Applications. 718:30-57

Subject Terms: FOS: Computer and information sciences, Eigenvalues, singular values, and eigenvectors, Discrete Mathematics (cs.DM), 05C50, 05E30, 11A07, 11A15, 11A25, Graphs and linear algebra (matrices, eigenvalues, etc.), spectra, Ramanujan functions, power residues, Arithmetic functions, related numbers, inversion formulas, circulant graphs, Graphs and abstract algebra (groups, rings, fields, etc.), Power residues, reciprocity, FOS: Mathematics, Association schemes, strongly regular graphs, Mathematics - Combinatorics, Congruences, primitive roots, residue systems, Combinatorics (math.CO), graph operations, Computer Science - Discrete Mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/2310.06203

Distribution of square free integers involving the floor function

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

Source: Periodica Mathematica Hungarica. :1-9

A generalisation of q-additive functions.

Authors: Mišík, Ladislav¹ (AUTHOR) Ladislav.Misik@osu.cz, Porubský, Štefan² (AUTHOR) sporubsky@hotmail.com

Source: Mathematica Slovaca. Jun2025, Vol. 75 Issue 3, p525-536. 12p.

Subject Terms: *ARITHMETIC functions, *NUMBER systems, *GENERALIZATION

On the number of points with bounded dynamical canonical height.

Authors: Takehira, Kohei¹ (AUTHOR) kohei.takehira.p5@dc.tohoku.ac.jp

Source: Journal of Number Theory. Jun2025, Vol. 271, p216-245. 30p.

Subject Terms: *ARITHMETIC functions, *NUMBER theory, *PROJECTIVE spaces, *SPECIAL functions, *ARITHMETIC

The Least Common Multiple of Consecutive Terms in the Cubic Progression {n3+4}n=1∞.

Authors: Fei, Shuanglin¹ (AUTHOR) Feishuanglin@126.com, Zhu, Guangyan² (AUTHOR) 2009043@hbmzu.edu.cn

Source: Algebra Colloquium. Jun2025, Vol. 32 Issue 2, p229-248. 20p.

Subject Terms: *ARITHMETIC functions, *PERIODIC functions, *INTEGERS, *POLYNOMIALS

On average behavior of a hybrid arithmetic function associated to Hecke eigenvalues of cusp forms over the values of a multivariate polynomial.

Authors: Sharma, Anubhav¹ (AUTHOR) anubhav6595@gmail.com, Sankaranarayanan, Ayyadurai² (AUTHOR) sank@uohyd.ac.in

Source: International Journal of Mathematics. Jun2025, Vol. 36 Issue 7, p1-20. 20p.

Subject Terms: *QUADRATIC forms, *ARITHMETIC functions, *VALUES (Ethics), *INTEGERS, *EIGENVALUES

Some structural aspects of the ring of arithmetical functions: Prime ideals and beyond.

Authors: Goswami, Amartya^1,2 (AUTHOR) agoswami@uj.ac.za, Kleyn, Danielle³ (AUTHOR) daniellem.kleyn@gmail.com, Porrill, Kerry³ (AUTHOR) kerry.porrill@gmail.com

Source: Journal of Algebra & Its Applications. May2025, p1. 16p.

Subject Terms: *PRIME ideals, *ARITHMETIC functions, *DIMENSION theory (Algebra), *NOETHERIAN rings, *IDEALS (Algebra), *MATHEMATICS

Implementation of Energy-Efficient Approximate Computing via Recursive Multiplier in Error-Tolerant Applications.

Authors: Karthikkumar, M.¹ (AUTHOR) mail2mkkumar@gmail.com, Kalaivani, R.¹ (AUTHOR) kalaitss72@yahoo.co.in

Source: Journal of Circuits, Systems & Computers. 5/15/2025, Vol. 34 Issue 7, p1-23. 23p.

Subject Terms: *ARITHMETIC functions, *IMAGE processing, *ARITHMETIC, *LOGIC

A generalized Ramanujan sum over a residually finite Dedekind domain.

Authors: Qi, T.¹ (AUTHOR) tfqiluck@njit.edu.cn

Source: Acta Mathematica Hungarica. Apr2025, Vol. 175 Issue 2, p333-351. 19p.

Subject Terms: *FINITE rings, *ARITHMETIC functions, *GENERALIZATION

Uniform distribution of polynomially-defined additive functions to varying moduli

Authors: Agbolade Akande

Source: International Journal of Number Theory. 21:959-973

Subject Terms: Other results on the distribution of values or the characterization of arithmetic functions, uniform distribution, additive function, residue classes, Mathematics - Number Theory, 11A25 (Primary) 11N64, 11N36 (Secondary), Arithmetic functions, related numbers, inversion formulas, exponential sums

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.04199
https://zbmath.org/8014156
https://doi.org/10.1142/s1793042125500484

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

File Description: application/xml

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

The provably total functions of basic arithmetic and its extensions: The provably total functions of basic arithmetic...: M. Ardeshir et al.

Authors: Ardeshir, Mohammad¹ (AUTHOR) mardeshir@sharif.edu, Khaniki, Erfan^2,3 (AUTHOR) khaniki@math.cas.cz, Shahriari, Mohsen¹ (AUTHOR) m.shahriari@sharif.edu

Source: Archive for Mathematical Logic. Feb2025, Vol. 64 Issue 1, p205-257. 53p.

Subject Terms: *PHILOSOPHY of mathematics, *ARITHMETIC functions, *CONSTRUCTIVE mathematics, *ARITHMETIC, *LOGIC

ON A PROBLEM OF PONGSRIIAM ON THE SUM OF DIVISORS.

Authors: WANG, RUI-JING¹ (AUTHOR) wangruijing271@163.com

Source: Bulletin of the Australian Mathematical Society. Feb2025, Vol. 111 Issue 1, p13-18. 6p.

Subject Terms: *ARITHMETIC functions, *INTEGERS, *MATHEMATICS, *ARITHMETIC series

ARITHMETIC PROPERTIES OF AN ANALOGUE OF t -CORE PARTITIONS.

Authors: TALUKDAR, PRANJAL¹ (AUTHOR) pranjaltalukdar113@gmail.com

Source: Bulletin of the Australian Mathematical Society. Feb2025, Vol. 111 Issue 1, p68-79. 12p.

Subject Terms: *PARTITION functions, *ARITHMETIC functions, *NUMBER theory, *MODULAR forms, *THETA functions, *GEOMETRIC congruences

Summatory Multiplicative Arithmetic Functions: Scaling and Renormalization.

Authors: Fel, Leonid G.¹ (AUTHOR) lfel@technion.ac.il

Source: Mathematics (2227-7390). Jan2025, Vol. 13 Issue 2, p281. 43p.

Subject Terms: *ASYMPTOTIC analysis, *ARITHMETIC functions, *DIRICHLET series, *NUMBER theory, *PRIME numbers