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arXiv · 1907.01116

Counting bounded elements of a number field

Mikołaj Frączyk·Gergely Harcos·Péter Maga
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Abstract

We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices. Our arguments combine group theory, ramification theory, and the geometry of numbers.

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Mikołaj Frączyk, Gergely Harcos, Péter Maga. 2019-07-02. Counting bounded elements of a number field. https://doi.org/10.1093/imrn%2Frnaa126

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