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Bi-quadratic fields having a non-principal Euclidean ideal class

Date: Thursday, October 31, 2019 10:30 - 11:00
Speaker: Jaitra Chattopadhyay (Harish-Chandra Research Institute)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Timothy Browning

Abstract:

In 1979, H. W. Lenstra defined the notion of an Euclidean ideal class and
proved that if a number field K has a non-principal Euclidean ideal class then the ideal class group ClK of K is cyclic. Except for the imaginary quadratic fields, he was able to prove the converse, under the assumption of GRH. Later, H. Graves constructed an explicit biquadratic field having an Euclidean ideal class and after a few years C.Hsu provided a family of such fields. In this talk, we shall give a new class of biquadratic fields other than the ones given by Graves and Hsu. This is a joint work with Dr. M. Subramani.
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