Bounds on the gaps in the fractional parts of a linear form
Copyright policy )Bounds on the gaps in the fractional parts of a linear form
We provide bounds on the sizes of the gaps—defined broadly—in the set { k 1 β 1 + … + k n β n (mod 1) : k i ∈ Z ∩ ( 0 , Q 1 n ] } \{k_1\boldsymbol \beta _1 + \ldots + k_n\boldsymbol \beta _n \text { (mod 1)} : k_i \in \mathbb {Z}\cap (0,Q^\frac {1}{n}]\} for generic β 1 , … , β n ∈ R m \boldsymbol \beta _1, \ldots , \boldsymbol \beta _n \in \mathbb {R}^m and all sufficiently large Q Q . We also introduce a related problem in Diophantine approximation, which we believe is of independent interest.
Mathematics - Number Theory, Diophantine approximation, FOS: Mathematics, Number Theory (math.NT), Dynamical Systems (math.DS), Geometry of numbers, Mathematics - Dynamical Systems, Diophantine approximation, transcendental number theory, three-gap theorem, geometry of numbers
Mathematics - Number Theory, Diophantine approximation, FOS: Mathematics, Number Theory (math.NT), Dynamical Systems (math.DS), Geometry of numbers, Mathematics - Dynamical Systems, Diophantine approximation, transcendental number theory, three-gap theorem, geometry of numbers
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!