Mean value estimates in lattice point theory |
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| Authors: | Dr Bohuslav Diviš |
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| Institution: | (1) Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210 Columbus, Ohio, USA |
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| 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
. By introduction of a parameter  we shall show how the treatment of estimates onP(x) and onM(x) can be unified. |
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