# Category Archives: math.NT

## Circle discrepancy for checkerboard measures

This week I am giving a talk at the Department of Mathematics and Systems Analysis of Aalto University where I will discuss results from a recent paper with Mihalis Kolountzakis. I will give a short introduction to different notions of … Continue reading

## The Rudin (Hardy-Littlewood) Conjecture, Notes 3: Omissions.

1. The set of squares does not contain arbitrarily long arithmetic progressions. As we have mentioned in the beginning of this discussion, Rudin was originally interested (among other things) in the number of terms the set of squares has in … Continue reading

## The Rudin (Hardy-Littlewood) Conjecture, Notes 2: A closer look at Λ(p)-sets.

This is the second post on Rudin’s conjecture. For the first introductory notes see here. In this post I will try to build some more intuition on -sets by studying some examples and discussing their properties. We will also discuss … Continue reading

## The Rudin (Hardy-Littlewood) Conjecture, Notes 1: Introduction and basic facts.

1. Introduction. This is the first of a series of posts concerning the Rudin-Hardy-Littlewood Conjecture. To give a taste of the problem right away let us consider to be a trigonometric polynomial of the form where for . The main … Continue reading

## The Discrepancy function in two dimensions.

Tomorrow I am traveling to Heraklion, Crete, where among other things I will give a talk on Discrepancy in two Dimensions. The talk is based on a recent paper with D. Bilyk, M. Lacey and A. Vaghasrhakyan. Here follows an … Continue reading