On the Construction of Galois Extensions of Function Fields and Number Fields.
On the Construction of Independent units in cyclic or radical extensions.
On the continued fractions of quadratic surds
On the convergence to 0 of mₙξmod 1
We show that for any irrational number α and a sequence of integers such that , there exists a continuous measure μ on the circle such that . This implies that any rigidity sequence of any ergodic transformation is a rigidity sequence for some weakly mixing dynamical system. On the other hand, we show that for any α ∈ ℝ - ℚ, there exists a sequence of integers such that and such that is dense on the circle if and only if θ ∉ ℚα + ℚ.
On the converse of Wolstenholme's Theorem
On the coprimality of certain multiplicative functions
On the Coprimality of Some Arithmetic Functions
On the coprimality of values of Euler's function at consecutive integers.
On the corner avoidance properties of various low-discrepancy sequences.
On the correlation of families of pseudorandom sequences of k symbols
In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.
On the correlation of Piltz functions.
On the correlation of the truncated Liouville function
On the counting function for sums of two squares
On the counting function for the generalized Niven numbers
Given an integer base and a completely -additive arithmetic function taking integer values, we deduce an asymptotic expression for the counting functionunder a mild restriction on the values of . When , the base sum of digits function, the integers counted by are the so-called base Niven numbers, and our result provides a generalization of the asymptotic known in that case.
On the counting function for the Niven numbers
On the Covering Multiplicity of Lattices.
On the critical determinants of certain star bodies
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 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 critical pair theory in ℤ/pℤ
On the critical values of certain Dirichlet series and the periods of automorphic forms.
On the critical values of Hecke L-functions for imaginary quadratic fields.