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

2 votes
1 answer
193 views

Cusp forms of weight 2 and level $\Gamma_0(p)$ where $p < 11$

Using Hida theory, we can prove that there is a cusp form of weight 2 and level $\Gamma_0(11)$. Are there ways to prove that there is no cusp forms of weight 2 and level $\Gamma_0(p)$ where $p < 11$? …
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1 vote
1 answer
130 views

Existence of tamely ramified tower of extension over $\mathbb{Q}_p$

Let $p$ be a prime. There exist following containment : $$\mathbb{Q}_p \subset \mathbb{Q}_p^{\rm nr} \subset \mathbb{Q}_p^{\rm tr} \subset \overline{\mathbb{Q}}_p$$ Here $\mathbb{Q}_p^{\rm nr}$ and $\ …
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  • 133