### 2009 Publications

#### Close lattice points on circles (with Javier Cilleruelo) Canadian Journal of Mathematics, (2009), 1214-1238.

We classify the sets of four lattice points that all lie on a short arc of a circle that has its center at the origin; specifically on arcs of length $$tR^{1/3}$$ on a circle of radius $$R$$, for any given $$t>0$$.

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#### Visibility in the plane (with Sukumar Das Adhikari) Journal of Number Theory, 129 (2009), 2335-2345.

We find the size of the smallest subset of the set of integer lattice points, such that every element of a given rectangular grid is visible from our subset, which answers a question of Paul Erdos.

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#### Pretentiousness in analytic number theory Journal de Théorie de nombres de Bordeaux, 21 (2009),159--173.

This is a written version of my lecture at the Journée Arithmétique in Edinburgh, in which I describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of "pretentiousness" to help us better understand several key questions in analytic number theory.

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