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Results tagged with nt.number-theory
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user 121540
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
4
votes
0
answers
204
views
Analytic continuation of a certain Euler product
What is known about analytic continuation of the following product ($\forall p:u_p\in\mathbb{C}$ with $|u_p |\leq 1$):
$\prod\limits_{p\in\mathbb{P}}
\left(
1-u_p p^{-s}
\right)^{-1}$
Clearly, I a …
- 139
1
vote
0
answers
254
views
Effective Hilbert's Irreducibility Theorem and Irreducibility of $f(x)+1$, $f(x)\in\mathbb{Q...
Take a reducible polynomial $f(x)\in\mathbb{Q}[x]$. I am interested in the question: is $f(x)+1$ irreducible over $\mathbb{Q}$?
For $f (x) = (x −a_1) · · · (x −a_m)$ with distinct $a_1,\ldots, a_m\in …
- 139