Euclidean algorithm and Kummer covers with many points.
Based on a method of H. W. Lenstra Jr. in this note 143 new Euclidean number fields are given of degree and 10 and of unit rank . The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.
Let be the moduli space of -pointed Riemann surfaces of genus . Denote by the Deligne-Mumford compactification of . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of for any and such that .