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Displaying 201 – 220 of 374

On the binary expansions of algebraic numbers

David H. Bailey, Jonathan M. Borwein, Richard E. Crandall, Carl Pomerance (2004)

Journal de Théorie des Nombres de Bordeaux

Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1’s in the binary expansions of real algebraic numbers. A central result is that if a real $y$ has algebraic degree $D > 1$ , then the number $# (| y |, N)$ of 1-bits in the expansion of $| y |$ through bit position $N$ satisfies $# (| y |, N) > C N^{1 / D}$ for a positive number $C$ (depending on $y$ ) and sufficiently large $N$ . This in itself establishes the transcendency of a class of reals $\sum_{n \geq 0} 1 / 2^{f (n)}$ where the integer-valued...

On the distribution of the sequence (nα) with transcendental α

Christoph Baxa (1997)

Acta Arithmetica

On the Gelfond-Feldman measure of algebraic independence

W. Dale Brownawell (1979)

Compositio Mathematica

On the greatest prime factor of $(a x^{m} + b y^{n})$

T. Shorey (1980)

Acta Arithmetica

On the greatest prime factors of polynomials at integer points

T. N. Shorey, R. Tijdeman (1976)

Compositio Mathematica

On the Oesterlé-Masser Conjecture.

C.L. Stewart, R. Tijdemann (1986)

Monatshefte für Mathematik

On the order function of a transcendental number

K. Mahler (1971)

Acta Arithmetica

On the orders of zero of certain functions

W. Dale Brownawell (1980)

Mémoires de la Société Mathématique de France

On the Possibility of Finding Certain Criteria for the Irrationality of a Number Defined as a Limit of a Sequence of Rational Numbers.

Viggo Brun, Finn F. Knudsen (1972)

Mathematica Scandinavica

On the quasi-periodic $p$ -adic Ruban continued fractions

Basma Ammous, Nour Ben Mahmoud, Mohamed Hbaib (2022)

Czechoslovak Mathematical Journal

We study a family of quasi periodic $p$ -adic Ruban continued fractions in the $p$ -adic field $ℚ_{p}$ and we give a criterion of a quadratic or transcendental $p$ -adic number which based on the $p$ -adic version of the subspace theorem due to Schlickewei.

ON the transcendence and algebraic independence of certain somewhat amusing numbers (results of Loxton and van der Poorten).

Alfred POORTEN van der (1975/1976)

Seminaire de Théorie des Nombres de Bordeaux

Currently displaying 201 – 220 of 374

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Displaying 201 – 220 of 374

On the binary expansions of algebraic numbers

On the distribution of the sequence (nα) with transcendental α

On the Gelfond-Feldman measure of algebraic independence

On the greatest prime factor of $(a x^{m} + b y^{n})$

On the greatest prime factors of polynomials at integer points

On the Oesterlé-Masser Conjecture.

On the order function of a transcendental number

On the orders of zero of certain functions

On the Possibility of Finding Certain Criteria for the Irrationality of a Number Defined as a Limit of a Sequence of Rational Numbers.

On the quasi-periodic $p$ -adic Ruban continued fractions

On the simultaneous approximation of $a$ , $b$ and $a^{b}$

On the simultaneous approximation of certain numbers.

On the simultaneous diophantine approximation of values of certain hypergeometric and algebraic functions

ON the transcendence and algebraic independence of certain somewhat amusing numbers (results of Loxton and van der Poorten).

On the transcendence of certain power series of algebraic numbers

On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers

On the values of a class of analytic functions at algebraic points

p-adic T-numbers do exist

p-adische Kettenbrüche und Irrationalität p-adischer Zahlen.

Pairs of polynomials small at a number to certain algebraic powers

Currently displaying 201 – 220 of 374