1
vote
1answer
58 views

Are all transcendental numbers theoretically accessible?

I apologize if the title (and the body) of this question is worded incorrectly, but I have no real experience in (transcendental) number theory, so it's probably the best I can do. I've been thinking ...
1
vote
0answers
46 views

Series of polynomials and uniformly convergence

It's part of the proof of a Lemma of an article I was reading (Algebraic values of transcendental functions at algebraic points). I couldn't understanding one thing: Let f be a complex function such ...
1
vote
1answer
18 views

Exceptional Set and Schanuel's conjecture

I was reading an article about transcendental funtions (Algebraic values of transcendental functions at algebraic points, by Huang, J., Marques, D., Mereb, M.). The authors gave an example that says: ...
4
votes
3answers
100 views

Real numbers that are not the roots of any polynomial equation with algebraic coefficients

An algebraic number is a number which is a root of some non-zero polynomial equation with rational coefficients. A transcendental number is a number which is not a root of any non-zero polynomial ...
2
votes
2answers
62 views

Transcendentals as the Roots of Infinite Polynomials

I have always been taught that the difference between an algebraic and a transcendental number is that the former is the root to a polynomial of ${\bf finite}$ degree with integer coefficients. I did ...
17
votes
1answer
540 views

Are $\pi$ and $e$ algebraically independent?

Update Edit : Title of this question formerly was "Is there a polynomial relation between $e$ and $\pi$?" Is there a polynomial relation (with algebraic numbers as coefficients) between $e$ or $\pi$ ...
42
votes
3answers
997 views
0
votes
2answers
241 views

Algebraic and Transcendental Numbers - Set Theory

Denote $\mathbb Q$$[x]$ = set of polynomials with coefficients $c_1$, $c_2$, $...$ ,$c_n$ in $\mathbb Q$. A number $a$ is algebraic if there exists a polynomial $f(x)$ in $\mathbb Q$[x] such that ...
3
votes
0answers
62 views

Schneider's theorem about the transcendence of values of the $j$-function

It is known that the $j$-function takes algebraic values when evaluated at imaginary quadratic integers. This is a result that was proved by Schneider in 1937 apparently. To be precise, Schneider ...