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Euclidean fields having a large Lenstra constant

Armin Leutbecher (1985)

Annales de l'institut Fourier

Based on a method of H. W. Lenstra Jr. in this note 143 new Euclidean number fields are given of degree n = 7 , 8 , 9 and 10 and of unit rank 5 . The search for these examples also revealed several other fields of small discriminant compared with the lower bounds of Odlyzko.

Euler characteristics of moduli spaces of curves

Gilberto Bini, John Harer (2011)

Journal of the European Mathematical Society

Let M g n be the moduli space of n -pointed Riemann surfaces of genus g . Denote by M g n ¯ the Deligne-Mumford compactification of M g n . In the present paper, we calculate the orbifold and the ordinary Euler characteristic of M g n ¯ for any g and n such that n > 2 - 2 g .

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