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.

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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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