Some properties of the class of arithmetic functions
R. P. Pakshirajan (1963)
Annales Polonici Mathematici
Similarity:
R. P. Pakshirajan (1963)
Annales Polonici Mathematici
Similarity:
Janusz Matkowski (2013)
Colloquium Mathematicae
Similarity:
A generalization of the weighted quasi-arithmetic mean generated by continuous and increasing (decreasing) functions , k ≥ 2, denoted by , is considered. Some properties of , including “associativity” assumed in the Kolmogorov-Nagumo theorem, are shown. Convex and affine functions involving this type of means are considered. Invariance of a quasi-arithmetic mean with respect to a special mean-type mapping built of generalized means is applied in solving a functional equation. For...
Antonio M. Oller-Marcén (2017)
Mathematica Bohemica
Similarity:
A homothetic arithmetic function of ratio is a function such that for every . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of in terms of the period and the ratio of .
Atsushi Moriwaki (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
Similarity:
In this paper, we give a numerical characterization of nef arithmetic -Cartier divisors of -type on an arithmetic surface. Namely an arithmetic -Cartier divisor of -type is nef if and only if is pseudo-effective and .
Laurent Habsieger, Xavier-François Roblot (2006)
Acta Arithmetica
Similarity:
Angkana Sripayap, Pattira Ruengsinsub, Teerapat Srichan (2022)
Czechoslovak Mathematical Journal
Similarity:
Let and . Denote by the set of all integers whose canonical prime representation has all exponents being a multiple of or belonging to the arithmetic progression , . All integers in are called generalized square-full integers. Using the exponent pair method, an upper bound for character sums over generalized square-full integers is derived. An application on the distribution of generalized square-full integers in an arithmetic progression is given. ...
Z. Kominek (1974)
Annales Polonici Mathematici
Similarity:
C. T. Ng (1973)
Annales Polonici Mathematici
Similarity:
Przemysław Mazur (2015)
Acta Arithmetica
Similarity:
We prove that every set A ⊂ ℤ satisfying for t and δ in suitable ranges must be very close to an arithmetic progression. We use this result to improve the estimates of Green and Morris for the probability that a random subset A ⊂ ℕ satisfies |ℕ∖(A+A)| ≥ k; specifically, we show that .
H. Światak (1967)
Annales Polonici Mathematici
Similarity:
M. Malenica (1982)
Matematički Vesnik
Similarity:
Roman Ger, Tomasz Kochanek (2009)
Colloquium Mathematicae
Similarity:
We show that any quasi-arithmetic mean and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations and are the constant ones.
Yasutaka Sibuya (1984)
Recherche Coopérative sur Programme n°25
Similarity:
Bakir Farhi (2013)
Colloquium Mathematicae
Similarity:
We present new structures and results on the set of mean functions on a given symmetric domain in ℝ². First, we construct on a structure of abelian group in which the neutral element is the arithmetic mean; then we study some symmetries in that group. Next, we construct on a structure of metric space under which is the closed ball with center the arithmetic mean and radius 1/2. We show in particular that the geometric and harmonic means lie on the boundary of . Finally, we give...
L. de Rosa, C. Segovia (2006)
Studia Mathematica
Similarity:
We study the boundedness of the one-sided operator between the weighted spaces and for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of . For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of from to , where denotes the operator M¯ iterated k times.
Min Zhang, Jianguo Si (2014)
Annales Polonici Mathematici
Similarity:
This work deals with Feigenbaum’s functional equation ⎧ , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.
Melvyn B. Nathanson, Kevin O'Bryant (2015)
Acta Arithmetica
Similarity:
A geometric progression of length k and integer ratio is a set of numbers of the form for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence of positive real numbers with a₁ = 1 such that the set contains no geometric progression of length k and integer ratio. Moreover, is a maximal subset of (0,1] that contains no geometric progression of length k and integer ratio. It is also proved that...
José del Carmen Alberto-Domínguez, Gerardo Acosta, Maira Madriz-Mendoza (2023)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We consider the Golomb and the Kirch topologies in the set of natural numbers. Among other results, we show that while with the Kirch topology every arithmetic progression is aposyndetic, in the Golomb topology only for those arithmetic progressions with the property that every prime number that divides also divides , it follows that being connected, being Brown, being totally Brown, and being aposyndetic are all equivalent. This characterizes the arithmetic progressions which are...
Enrique González-Jiménez (2015)
Acta Arithmetica
Similarity:
Let and a,q ∈ ℚ. Denote by the set of rational numbers d such that a, a + q, ..., a + (m-1)q form an arithmetic progression in the Edwards curve . We study the set and we parametrize it by the rational points of an algebraic curve.
Hasi Wulan, Kehe Zhu (2007)
Studia Mathematica
Similarity:
Under mild conditions on the weight function K we characterize lacunary series in the so-called spaces.
Mohammad Reza Jabbarzadeh, Rana Hajipouri (2017)
Mathematica Bohemica
Similarity:
First, some classic properties of a weighted Frobenius-Perron operator on as a predual of weighted Koopman operator on will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of under certain conditions.