All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 1120

Showing per page

A quantitative aspect of non-unique factorizations: the Narkiewicz constants II

Weidong Gao, Yuanlin Li, Jiangtao Peng (2011)

Colloquium Mathematicae

Let K be an algebraic number field with non-trivial class group G and K be its ring of integers. For k ∈ ℕ and some real x ≥ 1, let F k ( x ) denote the number of non-zero principal ideals a K with norm bounded by x such that a has at most k distinct factorizations into irreducible elements. It is well known that F k ( x ) behaves, for x → ∞, asymptotically like x ( l o g x ) 1 / | G | - 1 ( l o g l o g x ) k ( G ) . In this article, it is proved that for every prime p, ₁ ( C p ⊕ C p ) = 2 p , and it is also proved that ₁ ( C m p ⊕ C m p ) = 2 m p if ₁ ( C m ⊕ C m ) = 2 m and m is large enough. In particular, it is shown that for...

A short intervals result for linear equations in two prime variables.

M. B. S. Laporta (1997)

Revista Matemática de la Universidad Complutense de Madrid

Given A and B integers relatively prime, we prove that almost all integers n in an interval of the form [N, N+H], where N exp(1/3+e) ≤ H ≤ N can be written as a sum Ap1 + Bp2 = n, with p1 and p2 primes and e an arbitrary positive constant. This generalizes the results of Perelli et al. (1985) established in the classical case A=B=1 (Goldbach's problem).

A structure theorem for sets of small popular doubling

Przemysław Mazur (2015)

Acta Arithmetica

We prove that every set A ⊂ ℤ satisfying ∑ x m i n ( 1 A * 1 A ( x ) , t ) ≤ ( 2 + δ ) t | A | 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 ℙ ( | ℕ ∖ ( A + A ) | ≥ k ) = Θ ( 2 - k / 2 ) .

A ternary Diophantine inequality over primes

Roger Baker, Andreas Weingartner (2014)

Acta Arithmetica

Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality | p ₁ c + p ₂ c + p ₃ c - R | < R - η holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].

Currently displaying 61 – 80 of 1120