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## Correlations of the divisor function

- Lilian Matthiesen
- Mathematics
- 29 October 2010

Let τ(n)= ∑d 1d|n denote the divisor function. Employing the methods Green and Tao developed in their work on prime numbers, we give an asymptotic for the following correlation En∈[ −N,N… 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

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

- Lilian Matthiesen
- MathematicsJournal 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

## 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

## Generalized Fourier coefficients of multiplicative functions

- Lilian Matthiesen
- MathematicsAlgebra & Number Theory
- 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 ...

## Correlations of representation functions of binary quadratic forms

- Lilian Matthiesen
- Mathematics, Computer Science
- 18 May 2012

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

## Linear correlations of multiplicative functions

- Lilian Matthiesen
- MathematicsProceedings of the London Mathematical Society
- 14 June 2016

We prove a Green–Tao type theorem for multiplicative functions.

## There are uncountably many topological types of locally finite trees

- Lilian Matthiesen
- MathematicsJ. Comb. Theory, Ser. B
- 1 September 2006

## Frobenian multiplicative functions and rational points in fibrations

- D. Loughran, Lilian Matthiesen
- Mathematics
- 29 April 2019

We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rational point. We obtain lower bounds for this counting problem for some families over… Expand

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