lattice rest
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scholarly journals On the average order of the lattice rest of a convex body

1997 ◽  
Vol 80 (1) ◽  
pp. 89-100 ◽  
Author(s):  
Wolfgang Müller
Keyword(s):  
Convex Body ◽  
Average Order ◽  
Lattice Rest

On the lattice rest of a convex body in ?s, II

1986 ◽  
Vol 47 (3) ◽  
pp. 232-237 ◽  
Author(s):  
Werner Georg Nowak
Keyword(s):  
Convex Body ◽  
Lattice Rest

On the lattice rest of a convex body in ? s

1985 ◽  
Vol 45 (3) ◽  
pp. 284-288 ◽  
Author(s):  
Werner Georg Nowak
Keyword(s):  
Convex Body ◽  
Lattice Rest

An Ω-estimate for the lattice rest of a convex planar domain

1985 ◽  
Vol 100 (3-4) ◽  
pp. 295-299 ◽  
Author(s):  
Werner Georg Nowak
Keyword(s):  
Classical Result ◽  
Compact Convex ◽  
Lattice Points ◽  
Planar Domain ◽  
Circle Problem ◽  
Asymptotic Formulae ◽  
Lattice Rest ◽  
Image Position

SynopsisLet D be a compact convex planar domain containing the origin, the boundary of which is of class C∞ and has finite non-vanishing curvature throughout. For the number A(i) of lattice points in the “blown up” domain √tD, the estimateis established. This is a generalization of Hardy's classical result for the circle problem. The proof is based on asymptotic formulae for certain exponential integrals due to E. Hlawka.

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