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Results tagged with nt.number-theory
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user 31105
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
1
answer
352
views
Power free values of reducible polynomials
Browning in this paper proves that if $f \in \mathbb{Z}[x]$ is an irreducible polynomial of degree $d \geq 3$ and $k$ is an integer $\geq 3d/4 + 1/4$, then we have $$\#\{n \in \mathbb{Z} \cap [1, X] …
- 73
3
votes
2
answers
703
views
Inequality relating rank and analytic rank
Let $E$ be an elliptic curve over $\mathbb{Q}$. It is known from Gross and Zagier that if $\textrm{rank}_{\textrm{an}}(E) \leq 1$, then
$$\textrm{rank}(E) \geq \textrm{rank}_{\textrm{an}}(E).$$
Ins …
- 73