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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})=\ …
Nicco's user avatar
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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 …
Nicco's user avatar
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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 …
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