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Results tagged with nt.number-theory
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user 37998
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
7
votes
Probing the generalization of the abc conjecture to more than 3 variables
The relative primality certainly plays an important role. One can formulate a conjecture that accommodates the extent to which a particular summand is pairwise coprime, 3-wise coprime, etc, with other …
- 166
8
votes
Accepted
Exponential Sum Bound
First, the paper is Bruedern and Wooley!
Next ... by Cauchy's inequality, one has
$$|\Phi(\alpha)|^2\le 6H\Psi(\alpha),$$
say, where
$$\Psi(\alpha)=\sum_{h\le 6H}\left| \sum_{P<x\le 2P}e(\alpha h(3x^ …
- 166