Can a random lattice and its dual be independent?

Number Theory

17 March 18:15 - 19:15

Anders Södergren - Chalmers/University of Gothenburg

In this talk I will discuss Rogers' mean value formula in the space of unimodular lattices as well as a recent generalization of Rogers' formula. In particular, I will describe a formula for mean values of products of Siegel transforms with arguments taken from both a lattice and its dual lattice. The main application is a result on the joint distribution of the vector lengths in a random lattice and its dual lattice in the limit as the dimension of the lattices tends to infinity, and provides a partial affirmative answer to the question in the title. This is joint work with Andreas Strömbergsson.

Pär Kurlberg
KTH Royal Institute of Technology
Lilian Matthiesen
KTH Royal Institute of Technology
Damaris Schindler
Universität Göttingen


Pär Kurlberg

Lilian Matthiesen


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