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Results tagged with nt.number-theory
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user 24309
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
9
votes
Can the sum of two roots of unity be a root of unity?
True. For three terms $1+i-i=1$, all of which are $4^{th}$-root of $1$. For two terms you can also write $-\frac{1+\sqrt{3}i}{2}-\frac{1-\sqrt{3}i}{2}=-1$, all of which are $6^{th}$-root of $1$. And …
- 5,428
8
votes
1
answer
864
views
"Explicit" examples of Irrational numbers very well approximated by rational numbers
This question relates to this one and that one.
Some background
In the setting of discrete holomorphic dynamics (say, Julia sets)
an irrational $\lambda$ is said to be well approximated by rational
nu …
- 5,428
6
votes
Accepted
Can infinite polynomials be expressed as a product of its linear factors?
Hello Gabriel,
I think you should indeed have a look at the theory of (entire) holomorphic/meromorphic functions, since $x\mapsto (x-1)\zeta(x)$ belongs to that class. You more particularly wish to l …
- 5,428
2
votes
0
answers
147
views
Quadratic extension of an irrational number
Let $\alpha\in\mathbb R_{>2}\setminus\mathbb Q$ be an irrational number and let $\beta$ be such that
$$\alpha+\beta+\frac{1}{\beta}=0.$$
Is there a known relationship between the irrationality measure …
- 5,428