Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$

Binyamin Schwarz; Uri Srebro

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Displaying similar documents to “Carathéodory balls and norm balls in $H_{p, n} = z \in ℂ^{n} : ∥ z ∥_{p} < 1$ ”

The exceptional set of Goldbach numbers (II)

Hongze Li (2000)

Acta Arithmetica

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1. Introduction. A positive number which is a sum of two odd primes is called a Goldbach number. Let E(x) denote the number of even numbers not exceeding x which cannot be written as a sum of two odd primes. Then the Goldbach conjecture is equivalent to proving that E(x) = 2 for every x ≥ 4. E(x) is usually called the exceptional set of Goldbach numbers. In [8] H. L. Montgomery and R. C. Vaughan proved that $E (x) = O (x^{1 - Δ})$ for some positive constant Δ > 0 $. I n [3] C h e n a n d P a n p r o v e d t h a t o n e c a n t a k e Δ > 0.01 . I n [6], w e p r o v e d t h a t E (x) = O (x^{0.921})$ . In this paper we prove the following...

Gauss sum for the adjoint representation of $G L_{n} (q)$ and $S L_{n} (q)$

Yeon-Kwan Jeong, In-Sok Lee, Hyekyoung Oh, Kyung-Hwan Park (2000)

Acta Arithmetica

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On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm

Takao Komatsu (1998)

Acta Arithmetica

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We obtain the values concerning $(θ, ϕ) = l i m i n f_{| q | \to \infty} | q | ‖ q θ - ϕ ‖$ using the algorithm by Nishioka, Shiokawa and Tamura. In application, we give the values (θ,1/2), (θ,1/a), (θ,1/√(ab(ab+4))) and so on when θ = (√(ab(ab+4)) - ab)/(2a) = [0;a,b,a,b,...].

The homotopy groups of the L2 -localization of a certain type one finite complex at the prime 3

Yoshitaka Nakazawa, Katsumi Shimomura (1997)

Fundamenta Mathematicae

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For the Brown-Peterson spectrum BP at the prime 3, $v_{2}$ denotes Hazewinkel’s second polynomial generator of $B P_{*}$ . Let $L_{2}$ denote the Bousfield localization functor with respect to $v_{2}^{- 1} B P$ . A typical example of type one finite spectra is the mod 3 Moore spectrum M. In this paper, we determine the homotopy groups $π_{*} (L_{2} M \land X)$ for the 8 skeleton X of BP.

Note on the congruence of Ankeny-Artin-Chowla type modulo p²

Stanislav Jakubec (1998)

Acta Arithmetica

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The results of [2] on the congruence of Ankeny-Artin-Chowla type modulo p² for real subfields of $ℚ (ζ_{p})$ of a prime degree l is simplified. This is done on the basis of a congruence for the Gauss period (Theorem 1). The results are applied for the quadratic field ℚ(√p), p ≡ 5 (mod 8) (Corollary 1).

Property C'', strong measure zero sets and subsets of the plane

Janusz Pawlikowski (1997)

Fundamenta Mathematicae

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Let X be a set of reals. We show that • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections $F_{x}$ (x ∈ X) null, $\cup_{x \in X} F_{x}$ is null; • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections $F_{x}$ (x ∈ ℝ) null, $\cup_{x \in X} F_{x}$ is null.