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Results tagged with nt.number-theory
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user 36982
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
5
votes
0
answers
159
views
Multivariable multilinear homogeneous polynomials with co-prime coefficients representing 1
Suppose $F(x_1,\dots,x_n)$ is a homogeneous polynomial in $n$ variables of degree $m$, which has degree $1$ in each of the variables. Suppose further that it has integer relatively prime coefficients. …
- 255
11
votes
1
answer
636
views
An effective version of Kronecker's approximation theorem and its variations
Let $\theta_1,\dots,\theta_n$ be algebraic numbers of degree $\leq D$ and Weil height $\leq H$ such that $1,\theta_1,\dots,\theta_n$ are $\mathbb Q$-linearly independent. An effective version of Krone …
- 255
9
votes
1
answer
793
views
Distribution of moduli of quadratic residues
Let $D$ be a fixed positive squarefree integer. For a positive integer $x$, define
$S(D,x) = \{ q < x : D \text{is a quadratic residue} \pmod q \}$.
Here $q$ can be any integer, not necessarily a pr …
- 255