Characterization of norm forms via their values at integer points

George Tomanov

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arXiv · 2212.09734

Characterization of norm forms via their values at integer points

George Tomanov

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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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George Tomanov. 2022-12-19. Characterization of norm forms via their values at integer points. https://arxiv.org/abs/2212.09734

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