Lattice point problems and values of quadratic forms

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Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic (2004, background): “Ω(xp−2f(x)) for p>4, Ω(x2f(x)loglogx) for p= 4. V. Bentkus and F. Gotze [4], 1997: The estimate P(x;Ep) ≪ xp−2 for p≥ 9 holds for arbitrary ellipsoids. This result was extended to p≥ 5 by F. Gotze [26], 2004. V. Bentkus and F. Gotze [5], 1999: The estimate P(x;Ep) = o(xp−2) for p≥ 9 holds for irr”
On lattice points in large convex bodies (2010, background): “Bentkus and Götze [1] proved the conjecture for general ellipsoids in dimension d ≥ 9, and their result was improved to d ≥ 5 in Götze [3].”