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Results tagged with nt.number-theory
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user 88133
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
Complexity of a polynomial
Let $k_1,\dotsc,k_r$ be the even integers with even $2$-adic valuation in the range you want. For any polynomial $p$ meeting your condition, $p(x)-2^{n-1}$ has a root between $k_i-2$ and $k_i$, and a …
- 6,237
3
votes
There is a nice theory of quadratic forms. How about cubic forms, quartic forms, quintic for...
Here is an additional comment. Every homogeneous polynomial can be regarded as a symmetric tensor. Quadrics correspond to symmetric matrices; cubics correspond to order $3$ tensors; in general, a homo …
- 6,237
1
vote
Accepted
Conjectures inspired in the context of Casas-Alvero conjecture, via the logarithmic derivati...
I'm probably making a stupid mistake, but is Conjecture 1 possibly rather easy? At $\ell=0$ we're assuming
$$ p(x) = \frac{a_n}{n!} \left( \frac{n}{\frac{d}{dx} \log p(x)} \right)^n $$
Write $\frac{d} …
- 6,237