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On Minkowski units constructed by special values of Siegel modular functions

Takashi Fukuda, Keiichi Komatsu (2003)

Journal de théorie des nombres de Bordeaux

Using the special values of Siegel modular functions, we construct Minkowski units for the ray class field k 6 of ( e x p ( 2 π i / 5 ) ) modulo 6 . Our work is based on investigating the prime decomposition of the special values and describing explicitly the action of the Galois group G ( k 6 / ) for the special values. Futhermore we construct the full unit group of k 6 using modular and circular units under the GRH.

On mth order Bernoulli polynomials of degree m that are Eisenstein

Arnold Adelberg, Michael Filaseta (2002)

Colloquium Mathematicae

This paper deals with the irreducibility of the mth order Bernoulli polynomials of degree m. As m tends to infinity, Eisenstein's criterion is shown to imply irreducibility for asymptotically > 1/5 of these polynomials.

On multiple analogues of Ramanujan’s formulas for certain Dirichlet series

Hirofumi Tsumura (2008)

Journal de Théorie des Nombres de Bordeaux

In this paper, we prove multiple analogues of famous Ramanujan’s formulas for certain Dirichlet series which were introduced in his well-known notebooks. Furthermore, we prove some multiple versions of analogous formulas of Ramanujan which were given by Berndt and so on.

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