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Correlations of the divisor function

- Lilian Matthiesen
- Mathematics
- 29 October 2010

In this paper we study linear correlations of the divisor function tau(n) = sum_{d|n} 1 using methods developed by Green and Tao. For example, we obtain an asymptotic for sum_{n,d} tau(n) tau(n+d)… Expand

Norm forms for arbitrary number fields as products of linear polynomials

- T. Browning, Lilian Matthiesen
- Mathematics
- 29 July 2013

Let K/Q be a field extension of finite degree and let P(t) be a polynomial over Q that splits into linear factors over Q. We show that any smooth model of the affine variety defined by the equation… Expand

Linear correlations amongst numbers represented by positive definite binary quadratic forms

- Lilian Matthiesen
- Mathematics
- 23 June 2011

Given a positive definite binary quadratic form f, let r(n) = |{(x,y): f(x,y)=n}| denote its representation function. In this paper we study linear correlations of these functions. For example, if… Expand

Rational points on pencils of conics and quadrics with many degenerate fibres

- T. Browning, Lilian Matthiesen, A. Skorobogatov
- Mathematics
- 2 September 2012

For any pencil of conics or higher-dimensional quadrics over the rationals, with all degenerate fibres defined over the rationals, we show that the Brauer-Manin obstruction controls weak… Expand

Correlations of representation functions of binary quadratic forms

- Lilian Matthiesen
- Mathematics
- 18 May 2012

This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.

Generalized Fourier coefficients of multiplicative functions

- Lilian Matthiesen
- Mathematics
- 5 May 2014

We introduce and analyze a general class of not necessarily bounded multiplicative functions, examples of which include the function n bar right arrow delta(omega(n)), where delta is an element of ...

ON THE SQUARE-FREE REPRESENTATION FUNCTION OF A NORM FORM AND NILSEQUENCES

- Lilian Matthiesen
- Mathematics
- Journal of the Institute of Mathematics of…
- 17 September 2014

We show that the restriction to square-free numbers of the representation function attached to a norm form does not correlate with nilsequences. By combining this result with previous work of… Expand

There are uncountably many topological types of locally finite trees

- Lilian Matthiesen
- Computer Science, Mathematics
- J. Comb. Theory, Ser. B
- 1 September 2006

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Linear correlations of multiplicative functions

- Lilian Matthiesen
- Mathematics
- 14 June 2016

We prove a Green–Tao theorem for multiplicative functions.

A consequence of the factorisation theorem for polynomial orbits on nilmanifolds

- Lilian Matthiesen
- Mathematics
- 20 September 2015

We discuss a consequence of Green and Tao's factorisation theorem for polynomial orbits on nilmanifolds, adjusted to the requirements of certain arithmetic applications. More precisely, we prove a… Expand

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