On Hirzebruch sums and a theorem of Schinzel
Displaying 61 – 80 of 227
On Hurwitzian and Tasoev's continued fractions
Takao Komatsu (2003)
Acta Arithmetica
On inhomogeneous Diophantine approximation and the Nishioka-Shiokawa-Tamura algorithm
Takao Komatsu (1998)
Acta Arithmetica
We obtain the values concerning 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,...].
On inhomogeneous diophantine approximation with some quasi-periodic expressions, II
Takao Komatsu (1999)
Journal de théorie des nombres de Bordeaux
We consider the values concerningwhere the continued fraction expansion of has a quasi-periodic form. In particular, we treat the cases so that each quasi-periodic form includes no constant. Furthermore, we give some general conditions satisfying .
On integers generated by a finite number of fixed primes
R. Tijdeman, H. G. Meijer (1974)
Compositio Mathematica
On irrationality measures of the values of Gauss hypergeometric function.
A. Heimonen, Tapani Matala-Aho (1993)
Manuscripta mathematica
On irrationality of the values of certain series
Iekata SHIOKAWA (1980/1981)
Seminaire de Théorie des Nombres de Bordeaux
On irregularities of distribution, III
K. Roth (1979)
Acta Arithmetica
On irregularities of distribution, IV
K. Roth (1980)
Acta Arithmetica
On Kronecker's limit formula for Dirichlet series with periodic coefficients
Takeo Funakura (1990)
Acta Arithmetica
On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation
Michael Fuchs, Dong Han Kim (2016)
Acta Arithmetica
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent...
On Legendre's theorem related to diophantine approximations
S. ITO (1987/1988)
Seminaire de Théorie des Nombres de Bordeaux
On limit points of subsequences of uniformly distributed sequences
Ladislav Mišík (2014)
Acta Arithmetica
Given a subsequence of a uniformly distributed sequence, relations between the asymptotic densities of sets of its indices and the Lebesgue measure of the set of all its limit points are studied.
On linear forms in the logarithms of algebraic numbers
T. Shorey (1976)
Acta Arithmetica
On linear forms of a certain class of G-functions and p-adic G-functions
Keijo Väänänen (1980)
Acta Arithmetica
On linear forms of G-functions
K. Väänänen, Xu Guangshan (1988)
Acta Arithmetica
On Lower Bounds for Polynomials in the Values of E-Functions.
Keijo Väänänen (1977)
Manuscripta mathematica
On metric Diophantine approximation in positive characteristic
Kae Inoue, Hitoshi Nakada (2003)
Acta Arithmetica
On metric diophantine approximation of complex numbers, complex continued fractions
H. NAKADA (1987/1988)
Seminaire de Théorie des Nombres de Bordeaux
On metric theory of Diophantine approximation for complex numbers
Zhengyu Chen (2015)
Acta Arithmetica
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...