Abstract
LetQ(u) be a positive definite quadratic form inr≥2 variables with a real symmetric coefficient matrix of determinantD. Given a real vectorb with 0≤b j <1, forx>0 letA(x) be the number of lattice points in the ellipsoidQ(u+b)≤x, letV(x) be the volume of this ellipsoid andP(x)=A(x)−V(x). Let\(M(x) = \int\limits_0^x {P^2 (y)dy} \). By introduction of a parameter ϖ we shall show how the treatment of estimates onP(x) and onM(x) can be unified.
Keywords
Quadratic Form Lattice Point Coefficient Matrix Point Theory Positive Definite Quadratic Form
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References
- [1]Diviš, B.: Lattice point theory of irrational ellipsoids with an arbitrary center. Mh. Math.83, 279–307 (1977).Google Scholar
- [2]Diviš, B.: Ω-estimates in lattice point theory. (To appear.)Google Scholar
- [3]Novak, B.: Mean value theorems in the theory of lattice points with weight II. Comm. Math. Univ. Carol.11, 53–81 (1970).Google Scholar
Copyright information
© Springer-Verlag 1977