The k ‐dimensional Duffin and Schaeffer conjecture
نویسندگان
چکیده
منابع مشابه
The Duffin-schaeffer Conjecture with Extra Divergence
Throughout this note we will use the following standard notation from elementary number theory: p denotes a prime number, μ(n) is the Möbius function, φ(n) is the Euler phi function, ω(n) denotes the number of distinct prime divisors of n, and τ(n) is the number of positive integers which divide n. Also we use λ to denote Lebesgue measure on R/Z and dimX to denote the Hausdorff dimension of a s...
متن کاملThe Markoff-Duffin-Schaeffer inequalities abstracted.
The kth Markoff-Duffin-Schaeffer inequality provides a bound for the maximum, over the interval -1 </= x </= 1, of the kth derivative of a normalized polynomial of degree n. The bound is the corresponding maximum of the Chebyshev polynomial of degree n, T = cos(n cos(-1)x). The requisite normalization is over the values of the polynomial at the n + 1 points where T achieves its extremal values....
متن کاملTHE METRIC THEORY OF p−ADIC APPROXIMATION
Abstract. Metric Diophantine approximation in its classical form is the study of how well almost all real numbers can be approximated by rationals. There is a long history of results which give partial answers to this problem, but there are still questions which remain unknown. The Duffin-Schaeffer Conjecture is an attempt to answer all of these questions in full, and it has withstood more than...
متن کاملA note on zero-one laws in metrical Diophantine approximation
q ψ(q) diverges but A(ψ) is of zero measure. In other words, without the monotonicity assumption, Khintchine’s theorem is false and the famous Duffin-Schaeffer conjecture provides the appropriate statement. The key difference is that in (1), we impose coprimality on the integers p and q. Let A(ψ) denote the resulting subset of A(ψ). The Duffin-Schaeffer conjecture states that the measure of A(ψ...
متن کاملOn the X = M = K Conjecture
In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka polynomials. This is called the X = M = K conjecture. It is proved for tensor products of the “symmetric power” Kirillov-Reshetikhin modules for all nonexceptio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematika
سال: 1990
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579300012900