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Displaying 41 – 60 of 67

On the critical determinants of certain star bodies

Werner Georg Nowak (2017)

Communications in Mathematics

In a classic paper, W.G. Spohn established the to-date sharpest estimates from below for the simultaneous Diophantine approximation constants for three and more real numbers. As a by-result of his method which used Blichfeldt’s Theorem and the calculus of variations, he derived a bound for the critical determinant of the star body $| x_{1} | ({| x_{1} |}^{3} + {| x_{2} |}^{3} + {| x_{3} |}^{3}) \leq 1 .$ In this little note, after a brief exposition of the basics of the geometry of numbers and its significance for Diophantine approximation, this latter result is improved...

On the decomposition of vectors over number fields.

Edward B. Burger, Jeffrey D. Vaaler (1993)

Journal für die reine und angewandte Mathematik

On the Euclidean minimum of some real number fields

Eva Bayer-Fluckiger, Gabriele Nebe (2005)

Journal de Théorie des Nombres de Bordeaux

General methods from [3] are applied to give good upper bounds on the Euclidean minimum of real quadratic fields and totally real cyclotomic fields of prime power discriminant.

On the gaps of the Lagrange spectrum

Bernhard Dietz (1985)

Acta Arithmetica

On the Gaussian Markoff spectrum.

Henry W. Hansen (1978)

Mathematica Scandinavica

On the index of the boundary points of four-dimensional lattices that are admissible for a cube.

Smirnov, Yu.A. (2005)

Journal of Mathematical Sciences (New York)

On the lattice packing--covering ratio of finite-dimensional normed spaces

W. Banaszczyk (1990)

Colloquium Mathematicae

On the lattice point theory of multidimensional ellipsoids

B. Diviš, B. Novák (1974)

Acta Arithmetica

On the lattice rest of a convex body in $𝐑^{s}$ , III

Werner Georg Nowak (1991)

Czechoslovak Mathematical Journal

On the limit distribution of Frobenius numbers

Andreas Strömbergsson (2012)

Acta Arithmetica

On the Lower Markov Spectrum.

Mary E. Gbur (1976)

Monatshefte für Mathematik

On the magnitudes of some small cyclotomic integers

Frederick Robinson, Michael Wurtz (2013)

Acta Arithmetica

We prove the last of five outstanding conjectures made by R. M. Robinson from 1965 concerning small cyclotomic integers. In particular, given any cyclotomic integer β all of whose conjugates have absolute value at most 5, we prove that the largest such conjugate has absolute value of one of four explicit types given by two infinite classes and two exceptional cases. We also extend this result by showing that with the addition of one form, the conjecture is true for β with magnitudes up to 5 + 1/25....

Currently displaying 41 – 60 of 67

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Displaying 41 – 60 of 67

On the critical determinants of certain star bodies

On the decomposition of vectors over number fields.

On the Euclidean minimum of some real number fields

On the gaps of the Lagrange spectrum

On the Gaussian Markoff spectrum.

On the index of the boundary points of four-dimensional lattices that are admissible for a cube.

On the lattice packing--covering ratio of finite-dimensional normed spaces

On the lattice point theory of multidimensional ellipsoids

On the lattice rest of a convex body in $𝐑^{s}$ , III

On the limit distribution of Frobenius numbers

On the Lower Markov Spectrum.

On the magnitudes of some small cyclotomic integers

On the Maximum of the Minimum of a Sum.

On the minimum of the unit lattice

On the Number of Convex Lattice Polytopes.

On the number of lattice points inside a closed curve

On the Number of Primitive Lattice Points in Plane Domains.

On the packing densities of superballs and other bodies.

On the parity of the number of lattice points in certain tetrahedra.

On the proof of Humbert's volume formula.

Currently displaying 41 – 60 of 67