Characterization of norm forms via their values at integer points

2022/12/19 by George Tomanov, Tomanov, George
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2212.09734

Abstract

Using homogeneous dynamical approach, we obtain a complete description of the forms with discrete set of values at the integer points and not representing zero non-trivially over the rational numbers. As a consequence, we obtain a general class of non-purely real forms for which the natural generalization of Cassels and Swinnerton-Dyer conjecture fails.

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