Results 11 to 20 of about 379 (34)
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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On The Relative Class Number of Special Cyclotomic Fields [PDF]
, 2012 Let p be an odd prime, p be a primitive pth root of unity and h p be the relative class number of the pth cyclotomic fi eld Q( p) over the rationals Q defi ned by p.
Agoh, Takashi
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Characterization of the numbers which satisfy the height reducing property
, 2014 Let $\alpha$ be a complex number. We show that there is a finite subset $F$ of the ring of the rational integers $\mathbb{Z}$, such that $F\left[ \alpha\right] =\mathbb{Z}\left[ \alpha\right]$, if and only if $\alpha$ is an algebraic number whose ...
Akiyama, Shigeki +2 more
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Heights, Regulators and Schinzel's determinant inequality
, 2016 We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by ...
Akhtari, Shabnam, Vaaler, Jeffrey D.
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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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On Mertens-Ces\`aro Theorem for Number Fields
, 2015 Let $K$ be a number field with ring of integers $\mathcal O$. After introducing a suitable notion of density for subsets of $\mathcal O$, generalizing that of natural density for subsets of $\mathbb Z$, we show that the density of the set of coprime $m ...
Ferraguti, Andrea, Micheli, Giacomo
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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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The primitive ideal space of the C*-algebra of the affine semigroup of algebraic integers
, 2012 We give a complete description of the primitive ideal space of the C*-algebra associated to the ring of integers R in a number field K as considered in a recent paper by Cuntz, Deninger and ...
Cuntz +7 more
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Hasse-Minkowski theorem for quadratic forms on Mordell-Weil type groups
, 2017 In this paper we investigate an analogue of Hasse-Minkowski theorem for quadratic forms on Mordell-Weil type groups over number fields like $S$-units, abelian varieties with trivial ring of endomorphisms and odd algebraic $K$-theory ...
Barańczuk, Stefan
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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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