On metric theorems in the theory of uniform distribution
On metric theory of Diophantine approximation for complex numbers
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 . As one of partial results, in 1978, J. D. Vaaler proved this conjecture under the additional condition . 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 that a Vaaler...
On metrical theory of diophantine approximation over imaginary quadratic field
On minimal solutions of Diophantine equations.
On Minkowski units constructed by special values of Siegel modular functions
Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field of modulo . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group for the special values. Futhermore we construct the full unit group of using modular and circular units under the GRH.
On Mirsky's generalisation of a problem of Evelyn-Linfoot and Page in additive theory of numbers.
On mod logarithms and .
On modifying constructed normal numbers
On Modular Forms Associated with Indefinite Quadratic Forms of Signature (2, n ?2).
On Modular Forms whose Fourier Coefficients are Non-Negative Integers with the Constant Term Unity.
On modular functions in 2 variables attached to a family of hyperelliptic curves of genus 3
On modular representations of Gal (.../Q) arising from modular forms.
On modular units.
On monochromatic sets of integers whose diameters form a monotone sequence.
On monochromatic solutions of equations in groups.
On monochromatic subsets of a rectangular grid.
On monogenity of certain pure number fields of degrees
Let be a pure number field generated by a complex root of a monic irreducible polynomial , where , , are three positive natural integers. The purpose of this paper is to study the monogenity of . Our results are illustrated by some examples.
On Morita’s -adic -function
On mth order Bernoulli polynomials of degree m that are Eisenstein
This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.
On multiperiodic infinite recursions and their finite core.