Displaying similar documents to “Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion.”

Absolute norms of p -primary units

Supriya Pisolkar (2009)

Journal de Théorie des Nombres de Bordeaux

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We prove a local analogue of a theorem of J. Martinet about the absolute norm of the relative discriminant ideal of an extension of number fields. The result can be seen as a statement about 2 -primary units. We also prove a similar statement about the absolute norms of p -primary units, for all primes p .

A determinant formula for the relative class number of an imaginary abelian number field

Mikihito Hirabayashi (2014)

Communications in Mathematics

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We give a new formula for the relative class number of an imaginary abelian number field K by means of determinant with elements being integers of a cyclotomic field generated by the values of an odd Dirichlet character associated to K . We prove it by a specialization of determinant formula of Hasse.

Set of Points on Elliptic Curve in Projective Coordinates

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2011)

Formalized Mathematics

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In this article, we formalize a set of points on an elliptic curve over GF(p). Elliptic curve cryptography [10], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.