Note on an asymmetric diophantine approximation
نویسندگان
چکیده
منابع مشابه
A note on Diophantine approximation
Given a set of nonnegative real numbers Λ= {λi}i=0, a Λ-polynomial (or Müntz polynomial) is a function of the form p(x)=ni=0 aizi (n∈N). We denote byΠ(Λ) the space of Λ-polynomials and byΠZ(Λ) := {p(x)=ni=0 aizi ∈Π(λ) : ai ∈ Z for all i≥ 0} the set of integral Λ-polynomials. Clearly, the sets ΠZ(Λ) are subgroups of infinite rank of Z[x] wheneverΛ⊂N, #Λ=∞ (by infinite rank, wemean that the real ...
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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...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1946
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1946-08554-7