Combined approximations of some transcendental numbers

1990 ◽  
Vol 48 (5) ◽  
pp. 1163-1170
Author(s):  
A. A. Shmelev
Keyword(s):  
Transcendental Numbers ◽  
Combined Approximations

ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER

2016 ◽  
Vol 94 (1) ◽  
pp. 15-19 ◽  
Author(s):  
DIEGO MARQUES ◽  
JOSIMAR RAMIREZ
Keyword(s):  
Entire Functions ◽  
Complex Conjugation ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Transcendental Numbers ◽  
Lecture Notes ◽  
Transcendental Entire Functions

In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].

Estimates of Zeros of a Polynomial

1962 ◽  
Vol 58 (2) ◽  
pp. 229-234 ◽  
Author(s):  
L. Mirsky
Keyword(s):  
Integral Formula ◽  
Transcendental Numbers ◽  
Image Position ◽  
Complex Coefficients

Throughout this note we shall consider a fixed polynomial with complex coefficients and of degree n ≥ 2. Its zeros will be denoted by ξ1, ξ2, …, ξn where the numbering is such that Making use of Jensen's integral formula, Mahler (4) showed that, for l ≥ k < n, A slightly weaker result had been established by Feldman in an earlier publication (2). Mahler's inequality (1) is of importance in the study of transcendental numbers, and our first object is to sharpen his bound by proving the following result.

scholarly journals Contributions to the theory of transcendental numbers (II)

1968 ◽  
Vol 14 (1) ◽  
pp. 73-88 ◽  
Author(s):  
K. Ramachandra
Keyword(s):  
Transcendental Numbers

scholarly journals Contributions to the theory of transcendental numbers (I)

1968 ◽  
Vol 14 (1) ◽  
pp. 65-72 ◽  
Author(s):  
K. Ramachandra
Keyword(s):  
Transcendental Numbers

Transcendental Numbers in Wonderland

Math Horizons ◽  
2017 ◽  
Vol 24 (4) ◽  
pp. 22-23
Author(s):  
Eisuke Chikayama ◽  
Shori Chikayama
Keyword(s):  
Transcendental Numbers
Sign in / Sign up

Export Citation Format

Share Document