Abstract
Let be a nonzero algebraic integer of degree whose all conjugates lie in a sector , . We define the N-measure of by and the absolute N-measure of by . Firstly, we consider the case . We prove that and that, if is a reciprocal algebraic integer, is a square. Then, we study the set of the quantities . We prove that there exists a number such that is dense in . Finally, using the method of auxiliary functions, we find the seven smallest points of in . In case of , we compute the greatest lower bound of the absolute N-measure of , for belonging to eight subintervals of ]
Citation
Valérie Flammang. "The $N$-measure for algebraic integers having all their conjugates in a sector." Rocky Mountain J. Math. 50 (6) 2035 - 2045, December 2020. https://doi.org/10.1216/rmj.2020.50.2035
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