Results 1 to 10 of about 30 (30)
Ramanujan’s function k(τ)=r(τ)r2(2τ) and its modularity
Open Mathematics, 2020 We study the modularity of Ramanujan’s function k(τ)=r(τ)r2(2τ)k(\tau )=r(\tau ){r}^{2}(2\tau ), where r(τ)r(\tau ) is the Rogers-Ramanujan continued fraction.
Lee Yoonjin, Park Yoon Kyung
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An analogue in certain unique factorization domains of the Euclid‐Euler theorem on perfect numbers
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 1, Page 13-24, 1990., 1990 We show that there exists a natural extention of the sum of divisors function to all unique factorization domains F having a finite number of units such that if a perfect number in F is defined to be an integer η whose proper divisors sum to η, then the analogue of Euclid′s theorem giving the sufficient condition that an integer be an even perfect ...
Wayne L. McDaniel
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Matrices induced by arithmetic functions acting on certain Krein spaces
Special Matrices, 2017 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.
Cho Ilwoo
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Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
Special Matrices, 2015 In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
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Modular equations of a continued fraction of order six
Open Mathematics, 2019 We study a continued fraction X(τ) of order six by using the modular function theory. We first prove the modularity of X(τ), and then we obtain the modular equation of X(τ) of level n for any positive integer n; this includes the result of Vasuki et al ...
Lee Yoonjin, Park Yoon Kyung
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Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
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, 1998 5 páginas.-- 1991 Mathematics Subject Classification: 11R04, 11A05.Peer ...
Cilleruelo, Javier +3 more
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The product of a quartic and a sextic number cannot be octic
Open MathematicsIn this article, we prove that the product of two algebraic numbers of degrees 4 and 6 over Q{\mathbb{Q}} cannot be of degree 8. This completes the classification of so-called product-feasible triplets (a,b,c)∈N3\left(a,b,c)\in {{\mathbb{N}}}^{3} with a ...
Dubickas Artūras, Maciulevičius Lukas
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Reciprocal Monogenic Septinomials of Degree 2n3
Annales Mathematicae SilesianaeWe prove a new irreducibility criterion for certain septinomials in ℤ[x], and we use this result to construct infinite families of reciprocal septinomials of degree 2n3 that are monogenic for all n ≥ 1.
Jones Lenny
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Unit groups of some multiquadratic number fields and 2-class groups. [PDF]
Period Math Hung, 2022 Chems-Eddin MM.
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