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Bibliografias temáticas / K free integers

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Artigos de revistas

Literatura científica selecionada sobre o tema "K free integers"

Autor: Grafiati

Publicado: 29 de março de 2025

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Artigos de revistas sobre o assunto "K free integers"

1

Wu, Xia, and Yan Qin. "Rational Points of Elliptic Curve y2=x3+k3." Algebra Colloquium 25, no. 01 (2018): 133–38. http://dx.doi.org/10.1142/s1005386718000081.

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Let E be an elliptic curve defined over the field of rational numbers ℚ. Let d be a square-free integer and let Ed be the quadratic twist of E determined by d. Mai, Murty and Ono have proved that there are infinitely many square-free integers d such that the rank of Ed(ℚ) is zero. Let E(k) denote the elliptic curve y2 = x3 + k. Then the quadratic twist E(1)d of E(1) by d is the elliptic curve [Formula: see text]. Let r = 1, 2, 5, 10, 13, 14, 17, 22. Ono proved that there are infinitely many square-free integers d ≡ r (mod 24) such that rank [Formula: see text], using the theory of modular form

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2

Haukkanen, Pentti. "Arithmetical functions associated with conjugate pairs of sets under regular convolutions." Notes on Number Theory and Discrete Mathematics 28, no. 4 (2022): 656–65. http://dx.doi.org/10.7546/nntdm.2022.28.4.656-665.

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Two subsets P and Q of the set of positive integers is said to form a conjugate pair if each positive integer n possesses a unique factorization of the form n = ab, a ∈ P, b ∈ Q. In this paper we generalize conjugate pairs of sets to the setting of regular convolutions and study associated arithmetical functions. Particular attention is paid to arithmetical functions associated with k-free integers and k-th powers under regular convolution.

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3

Minh, Nguyen Quang. "A Generalisation of Maximal (k,b)-Linear-Free Sets of Integers." Journal of Combinatorial Mathematics and Combinatorial Computing 120, no. 1 (2024): 315–21. http://dx.doi.org/10.61091/jcmcc120-28.

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Fix integers k , b , q with k ≥ 2 , b ≥ 0 , q ≥ 2 . Define the function p to be: p ( x ) = k x + b . We call a set S of integers \emph{ ( k , b , q ) -linear-free} if x ∈ S implies p i ( x ) ∉ S for all i = 1 , 2 , … , q − 1 , where p i ( x ) = p ( p i − 1 ( x ) ) and p 0 ( x ) = x . Such a set S is maximal in [ n ] := { 1 , 2 , … , n } if S ∪ { t } , ∀ t ∈ [ n ] ∖ S is not ( k , b , q ) -linear-free. Let M k , b , q ( n ) be the set of all maximal ( k , b , q ) -linear-free subsets of [ n ] , and define g k , b , q ( n ) = min S ∈ M k , b , q ( n ) | S | and f k , b , q ( n ) = max S ∈ M k ,

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4

Liu, H. Q. "On the distribution of k-free integers." Acta Mathematica Hungarica 144, no. 2 (2014): 269–84. http://dx.doi.org/10.1007/s10474-014-0454-9.

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5

Wlazinski, Francis. "A uniform cube-free morphism is k-power-free for all integers k ≥ 4." RAIRO - Theoretical Informatics and Applications 51, no. 4 (2017): 205–16. http://dx.doi.org/10.1051/ita/2017015.

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6

Cellarosi, Francesco, and Ilya Vinogradov. "Ergodic properties of $k$-free integers in number fields." Journal of Modern Dynamics 7, no. 3 (2013): 461–88. http://dx.doi.org/10.3934/jmd.2013.7.461.

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7

Dong, D., and X. Meng. "Irrational Factor of Order k and ITS Connections With k-Free Integers." Acta Mathematica Hungarica 144, no. 2 (2014): 353–66. http://dx.doi.org/10.1007/s10474-014-0420-6.

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8

Choi, Dohoon, та Youngmin Lee. "Modular forms of half-integral weight on Γ₀(4) with few nonvanishing coefficients modulo ℓ". Open Mathematics 20, № 1 (2022): 1320–36. http://dx.doi.org/10.1515/math-2022-0512.

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Abstract Let k k be a nonnegative integer. Let K K be a number field and O K {{\mathcal{O}}}_{K} be the ring of integers of K K . Let ℓ ≥ 5 \ell \ge 5 be a prime and v v be a prime ideal of O K {{\mathcal{O}}}_{K} over ℓ \ell . Let f f be a modular form of weight k + 1 2 k+\frac{1}{2} on Γ 0 {\Gamma }_{0} (4) such that its Fourier coefficients are in O K {{\mathcal{O}}}_{K} . In this article, we study sufficient conditions that if f f has the form f ( z ) ≡ ∑ n = 1 ∞ ∑ i = 1 t a f ( s i n 2 ) q s i n 2 ( mod v ) f\left(z)\equiv \mathop{\sum }\limits_{n=1}^{\infty }\mathop{\sum }\limits_{i=1}^{

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9

LE BOUDEC, PIERRE. "POWER-FREE VALUES OF THE POLYNOMIAL t1⋯tr−1." Bulletin of the Australian Mathematical Society 85, no. 1 (2011): 154–63. http://dx.doi.org/10.1017/s0004972711002590.

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10

Benamar, Hela, Amara Chandoul, and M. Mkaouar. "On the Continued Fraction Expansion of Fixed Period in Finite Fields." Canadian Mathematical Bulletin 58, no. 4 (2015): 704–12. http://dx.doi.org/10.4153/cmb-2015-055-9.

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AbstractThe Chowla conjecture states that if t is any given positive integer, there are infinitely many prime positive integers N such that Per() = t, where Per() is the period length of the continued fraction expansion for . C. Friesen proved that, for any k ∈ ℕ, there are infinitely many square-free integers N, where the continued fraction expansion of has a fixed period. In this paper, we describe all polynomials for which the continued fraction expansion of has a fixed period. We also give a lower bound of the number of monic, non-squares polynomials Q such that deg Q = 2d and Per =t.

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