scholarly journals $\Omega $-results for the hyperbolic lattice point problem

2016 ◽  
Vol 145 (4) ◽  
pp. 1421-1437
Author(s):  
Dimitrios Chatzakos
Keyword(s):  
Lattice Point ◽  
Point Problem ◽  
Lattice Point Problem ◽  
Hyperbolic Lattice

scholarly journals The hyperbolic lattice point problem in conjugacy classes

2016 ◽  
Vol 28 (5) ◽  
pp. 981-1003
Author(s):  
Dimitrios Chatzakos ◽  
Yiannis N. Petridis
Keyword(s):  
Lattice Point ◽  
Quadratic Forms ◽  
Fuchsian Group ◽  
Riemann Surfaces ◽  
Conjugacy Classes ◽  
Point Problem ◽  
Large Sieve ◽  
Lattice Point Problem ◽  
Hyperbolic Lattice ◽  
Indefinite Quadratic

AbstractFor Γ a cocompact or cofinite Fuchsian group, we study the hyperbolic lattice point problem in conjugacy classes, which is a modification of the classical hyperbolic lattice point problem. We use large sieve inequalities for the Riemann surfaces ${{\Gamma\backslash{\mathbb{H}}}}$ to obtain average results for the error term, which are conjecturally optimal. We give a new proof of the error bound ${O(X^{2/3})}$, due to Good. For ${{\mathrm{SL}_{2}({\mathbb{Z}})}}$ we interpret our results in terms of indefinite quadratic forms.

Steinhaus' lattice point problem for polyhedra

2017 ◽  
Vol 146 (1) ◽  
pp. 123-128 ◽  
Author(s):  
Hiroshi Maehara
Keyword(s):  
Lattice Point ◽  
Point Problem ◽  
Lattice Point Problem

The Generalized Lattice-Point Problem

1973 ◽  
Vol 21 (1) ◽  
pp. 141-155 ◽  
Author(s):  
Fred Glover ◽  
D. Klingman
Keyword(s):  
Lattice Point ◽  
Point Problem ◽  
Lattice Point Problem
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