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On the existence of hyperrings associated to arithmetic functions

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1 Published in 2017 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2016.10.017

Abstract: Abstract After introducing the definition of hyperring by Krasner, the study of hyperrings has been of great importance. In this paper, we define a new hyperoperation associated to the set G of all arithmetic functions… read more here.

Keywords: arithmetic functions; hyperrings associated; hyperoperation; existence hyperrings ... See more keywords

Strongly regular relations of arithmetic functions

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0 Published in 2017 at "Journal of Number Theory"

DOI: 10.1016/j.jnt.2017.11.006

Abstract: Abstract A simple, but very useful concept in number theory is that of an arithmetic function. On the other hand, hyperstructure theory, first introduced by Marty, is a generalization of group theory and it is… read more here.

Keywords: arithmetic functions; theory; strongly regular; regular relations ... See more keywords

MEAN VALUES OF ARITHMETIC FUNCTIONS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS IN THE LARGE‐DEGREE LIMIT

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0 Published in 2020 at "Mathematika"

DOI: 10.1112/mtk.12032

Abstract: A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progression, with the interval as… read more here.

Keywords: large degree; arithmetic progressions; degree limit; interval ... See more keywords

Matrices induced by arithmetic functions acting on certain Krein spaces

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1 Published in 2017 at "Special Matrices"

DOI: 10.1515/spma-2017-0019

Abstract: Abstract In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers. read more here.

Keywords: arithmetic functions; acting certain; functions acting; induced arithmetic ... See more keywords

Inequalities with Some Arithmetic Functions

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0 Published in 2025 at "Mathematics"

DOI: 10.3390/math13081253

Abstract: In the paper, some new inequalities are formulated and proved with the classical arithmetic functions φ (of Euler) and ψ (of Dedekind). read more here.

Keywords: inequalities arithmetic; arithmetic functions;