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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

6 votes

Does pi contain 1000 consecutive zeroes (in base 10)?

I do not know what kind of effect this has on your question, but it might be a good thing to look at in this context. In 1995, a formula for the $n$-th digit of $\pi$ written in hexadecimal was found. …
4 votes

Expressing Galois actions on fundamental groups explicitly

I'm not precicely sure what you are looking for, but the following references I think are relevant. The Grothendieck Theory of Dessins d'Enfants (London Mathematical Society Lecture Note Series) LMs …
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