Irrational and Transcendental Numbers

2019 ◽  
pp. 348-365
2016 ◽  
Vol 94 (1) ◽  
pp. 15-19 ◽  
Author(s):  
DIEGO MARQUES ◽  
JOSIMAR RAMIREZ

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)].


1962 ◽  
Vol 58 (2) ◽  
pp. 229-234 ◽  
Author(s):  
L. Mirsky

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.


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

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

Math Horizons ◽  
2017 ◽  
Vol 24 (4) ◽  
pp. 22-23
Author(s):  
Eisuke Chikayama ◽  
Shori Chikayama

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