Add to ORKGIt is a classical result of Mahler that for any rational number α > 1 which is not an integer and any real 0 1, Hardy about a century ago asked "In what circumstances can it be true that λα n → 0 as n → ∞? " This question is still open in general. In this note, we study its analogue in the context of the problem of Mahler. We first compare and contrast with what is known visa -vis the original question of Hardy. We then suggest a number of questions that arise as natural consequences of our investigation. Of these questions, we answer one and offer some insight into others
The height of a rational number p/q is defined by max(|p|,|q|) provided p/q is written in lowest ter...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real nu...
It is a classical result of Mahler that for any rational number α > 1 which is not an integer and an...
Arealnumberβ>1 is said to satisfy Property (F) if every non-negative number of Z[β −1] has a fini...
Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven’s proof to show that e...
Rational approximations to π and some other numbers by Masayoshi Hata (Kyoto) 1. Introduction. In 19...
AbstractLet n be an integer ≥ 1 and let θ be a real number which is not an algebraic number of degre...
This paper proves the existence of an universal nontrivial minorant of the set of the Mahler measure...
Hilbert’s 10th problem asked: Give a procedure which, in a finite number of steps, can determine whe...
A problem of Mahler on farctional parts of powers of an algebraic number is solved, namely a classif...
AbstractGiven a rational functionRand a real numberp⩾1, we definehp(R) as theLpnorm of max{log|R|, 0...
International audienceThe present work proposes an attack of the Conjecture of Lehmer by the dynamic...
AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt...
Let K denote the middle third Cantor set and . Given a real, positive function ψ let denote the set...
The height of a rational number p/q is defined by max(|p|,|q|) provided p/q is written in lowest ter...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real nu...
It is a classical result of Mahler that for any rational number α > 1 which is not an integer and an...
Arealnumberβ>1 is said to satisfy Property (F) if every non-negative number of Z[β −1] has a fini...
Niven [3] gave a simple proof that π is irrational. Koksma [2] modified Niven’s proof to show that e...
Rational approximations to π and some other numbers by Masayoshi Hata (Kyoto) 1. Introduction. In 19...
AbstractLet n be an integer ≥ 1 and let θ be a real number which is not an algebraic number of degre...
This paper proves the existence of an universal nontrivial minorant of the set of the Mahler measure...
Hilbert’s 10th problem asked: Give a procedure which, in a finite number of steps, can determine whe...
A problem of Mahler on farctional parts of powers of an algebraic number is solved, namely a classif...
AbstractGiven a rational functionRand a real numberp⩾1, we definehp(R) as theLpnorm of max{log|R|, 0...
International audienceThe present work proposes an attack of the Conjecture of Lehmer by the dynamic...
AbstractLet β be an irrational number. For t ≥ 1, put ψβ(t)= minp,qint 0<q⩽t | qβ − p |, μ∗(β)= supt...
Let K denote the middle third Cantor set and . Given a real, positive function ψ let denote the set...
The height of a rational number p/q is defined by max(|p|,|q|) provided p/q is written in lowest ter...
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an...
Let k be an integer with 4≤k≤6 and η be any real number. Suppose that λ1,λ2,…,λ5 are nonzero real nu...