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Correlations of the divisor function
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
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 equationExpand
Linear correlations amongst numbers represented by positive definite binary quadratic forms
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, ifExpand
Rational points on pencils of conics and quadrics with many degenerate fibres
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 weakExpand
Correlations of representation functions of binary quadratic forms
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
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 ...
  • 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 ofExpand
There are uncountably many topological types of locally finite trees
  • Lilian Matthiesen
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1 September 2006
Answering a question of van der Holst, we prove that there are uncountably many equivalence classes for locally finite rooted trees. Expand
Linear correlations of multiplicative functions
We prove a Green–Tao theorem for multiplicative functions.
A consequence of the factorisation theorem for polynomial orbits on nilmanifolds
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 aExpand