On values of binary quadratic forms at integer points

Values of Binary Quadratic Forms at Integer Points and Schmidt Games

We prove that for any countable set A of real numbers, the set of binary indefinite quadratic forms Q such that the closure of Q ` Z2 ́ is disjoint from A has full Hausdorff dimension. Dedicated to S.G. Dani on the occasion of his 65th birthday

Values of isotropic quadratic forms at S-integral points

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Values of Quadratic Forms at Integral Points : an Elementary Approach

On the Gaps between Values of Binary Quadratic Forms

Among the values of a binary quadratic form, there are many twins of fixed distance. This is shown in quantitative form. For quadratic forms of discriminant −4 or 8 a corresponding result is obtained for triplets.

Simultaneous Integer Values of Pairs of Quadratic Forms

We prove that a pair of integral quadratic forms in 5 or more variables will simultaneously represent “almost all” pairs of integers that satisfy the necessary local conditions, provided that the forms satisfy a suitable nonsingularity condition. In particular such forms simultaneously attain prime values if the obvious local conditions hold. The proof uses the circle method, and in particular ...