On the critical determinants of certain star bodies

Werner Georg Nowak

Displaying similar documents to “On the critical determinants of certain star bodies”

Lower bounds for simultaneous Diophantine approximation constants

Werner Georg Nowak (2014)

Communications in Mathematics

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After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants $θ_{s}$ , new lower bounds are deduced for $θ_{6}$ and $θ_{7}$ .

On the Diophantine equation $X^{2} - (2^{2 m} + 1) Y^{4} = - 2^{2 m}$

Michael Stoll, P. G. Walsh, Pingzhi Yuan (2009)

Acta Arithmetica

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Explicit lower bounds for ${| | (3 / 2)}^{k} | |$

Laurent Habsieger (2003)

Acta Arithmetica

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On the Diophantine equation $x^{p} + y^{2 p} = z^{2}$

A. Rotkiewicz, A. Schinzel (1987)

Colloquium Mathematicae

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Method of infinite ascent applied on $- (2^{p} \cdot A^{6}) + B^{3} = C^{2}$

Susil Kumar Jena (2013)

Communications in Mathematics

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In this paper, the author shows a technique of generating an infinite number of coprime integral solutions for $(A, B, C)$ of the Diophantine equation $- (2^{p} \cdot A^{6}) + B^{3} = C^{2}$ for any positive integral values of $p$ when $p \equiv 1$ (mod 6) or $p \equiv 2$ (mod 6). For doing this, we will be using a published result of this author in The Mathematics Student, a periodical of the Indian Mathematical Society.

On metric theory of Diophantine approximation for complex numbers

Zhengyu Chen (2015)

Acta Arithmetica

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In 1941, R. J. Duffin and A. C. Schaeffer conjectured that for the inequality |α - m/n| < ψ(n)/n with g.c.d.(m,n) = 1, there are infinitely many solutions in positive integers m and n for almost all α ∈ ℝ if and only if $\sum_{n = 2}^{\infty} ϕ (n) ψ (n) / n = \infty$ . As one of partial results, in 1978, J. D. Vaaler proved this conjecture under the additional condition $ψ (n) = (n^{- 1})$ . In this paper, we discuss the metric theory of Diophantine approximation over the imaginary quadratic field ℚ(√d) with a square-free integer d < 0, and show...

Searching for Diophantine quintuples

Mihai Cipu, Tim Trudgian (2016)

Acta Arithmetica

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We consider Diophantine quintuples a, b, c, d, e. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441 \cdot 10^{26}$ Diophantine quintuples.

A note on the Diophantine equation $x^{2} + q^{m} = y^{3}$

Hui Lin Zhu (2011)

Acta Arithmetica

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A note on the number of $S$ -Diophantine quadruples

Florian Luca, Volker Ziegler (2014)

Communications in Mathematics

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Let $(a_{1}, \dots, a_{m})$ be an $m$ -tuple of positive, pairwise distinct integers. If for all $1 \leq i < j \leq m$ the prime divisors of $a_{i} a_{j} + 1$ come from the same fixed set $S$ , then we call the $m$ -tuple $S$ -Diophantine. In this note we estimate the number of $S$ -Diophantine quadruples in terms of $| S | = r$ .