engleski

The unit sum number problem in some number fields

In this talk we investigate the additive unit structure of some number fields. More precisely, we determine which pure complex quartic fields have the property that their integers can be represented as a sum of units. In the case of quadratic fields we find assymptotic formula for u_k(x, m), where u_k(x, m) is the number of non-associated integers with norm <= x that can be represented as a sum of m units.

additive structure of unit group; unit sum number

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