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Results tagged with nt.number-theory
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user 75820
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
15
votes
Ramanujan's $\tau(n)$ and continued fractions
Since the OP asked for other examples of this kind of numerology,I will give another one to support his observation
The function $\cos(\theta_{11})$ has the following closed form
$\cos(\theta_{11})=\ …
- 256
6
votes
Accepted
Are these two $q$-continued fractions equivalent?
In this answer we shall follow a path Ramanujan must have likely taken at some point, though we have no solid evidence that he actually did. We prove the claim in two different ways part I and Part II …
- 256
3
votes
0
answers
248
views
Continued fractions and modular forms
Let $q=e^{2\pi it}$. If $u(t)$ is Ramanujan's octic continued fraction, is it true that the generator of the octahedral group can be expressed as a continued fraction of the form
$$
(u(2t))^2=\frac{2q …
- 256