4 papers
Values of ternary quadratic forms at integers and the Berry-Tabor conjecture for 3-tori
Wooyeon Kim, Jens Marklof, Matthew Welsh
Berry and Tabor conjectured in 1977 that spectra of generic integrable quantum systems have the same local statistics as a Poisson point process. We verify their conjecture in the…
Representations of binary forms by quaternary quadratic forms
Wooyeon Kim, Andreas Wieser, Pengyu Yang
We prove a local-global principle for representations of binary by quaternary quadratic forms. One of the main ingredients is a recent measure rigidity result of Einsiedler and Lin…
Moments of Margulis functions and indefinite ternary quadratic forms
Wooyeon Kim
In this paper, we prove a quantitative version of the Oppenheim conjecture for indefinite ternary quadratic forms: for any indefinite irrational ternary quadratic form that is…
On divergent on average trajectories for higher rank actions
Wooyeon Kim
For we first show that the Hausdorff dimension of the set of -divergent on average points in the -dimensional closed horosphere in the space of -dimensional E…