Results 1 to 10 of about 360 (22)
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
doaj +1 more source
Divisors in a Dedekind domain [PDF]
, 1998 5 páginas.-- 1991 Mathematics Subject Classification: 11R04, 11A05.Peer ...
Avi Rosenfeld +12 more
core +1 more source
$k$th power residue chains of global fields [PDF]
, 2010 In 1974, Vegh proved that if $k$ is a prime and $m$ a positive integer, there is an $m$ term permutation chain of $k$th power residue for infinitely many primes [E.Vegh, $k$th power residue chains, J.Number Theory, 9(1977), 179-181].
Hu, Su, Li, Yan
core +3 more sources
Equidistribution of Elements of Norm 1 in Cyclic Extensions [PDF]
, 2014 Upon quotienting by units, the elements of norm 1 in a number field $K$ form a countable subset of a torus of dimension $r_1 + r_2 - 1$ where $r_1$ and $r_2$ are the numbers of real and pairs of complex embeddings.
Petersen, Kathleen L. +1 more
core +3 more sources
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
doaj +1 more source
On covers of abelian groups by cosets [PDF]
, 2008 Let G be any abelian group and {a_sG_s}_{s=1}^k be a finite system of cosets of subgroups G_1,...,G_k. We show that if {a_sG_s}_{s=1}^k covers all the elements of G at least m times with the coset a_tG_t irredundant then [G:G_t]\le 2^{k-m} and ...
Lettl, Günter, Sun, Zhi-Wei
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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
wiley +1 more source
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.
doaj +1 more source
A sharp result on m-covers [PDF]
, 2005 Let A={a_s+n_sZ}_{s=1}^k be a finite system of arithmetic sequences which forms an m-cover of Z (i.e., every integer belongs at least to m members of A). In this paper we show the following sharp result: For any positive integers m_1,...,m_k and theta in
Pan, Hao, Sun, Zhi-Wei
core +5 more sources
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
doaj +1 more source