2-adic and 3-adic part of class numbers and properties of central values of L-functions
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Matija Kazalicki (2011)
Acta Arithmetica
Mikaël Lescop (2004)
Acta Arithmetica
Daniel Allcock, Jeffrey D. Vaaler (2009)
Acta Arithmetica
H.L. Montgomery, J.C. Lagarias (1979)
Inventiones mathematicae
Soulé, Christophe (2003)
Documenta Mathematica
Ladislav Skula (2003)
Mathematica Slovaca
K. Ozeki (1982)
Aequationes mathematicae
K. Ozeki (1982)
Aequationes mathematicae
Ulrich Krause (1984)
Mathematische Zeitschrift
Henning Stichtenoth, Hans-Georg Rück (1994)
Journal für die reine und angewandte Mathematik
Denis Simon (2008)
Journal de Théorie des Nombres de Bordeaux
In this paper, we study equations of the form , where is a binary form, homogeneous of degree , which is supposed to be primitive and irreducible, and is any fixed integer. Using classical tools in algebraic number theory, we prove that the existence of a proper solution for this equation implies the existence of an integral ideal of given norm in some order in a number field, and also the existence of a specific relation in the class group involving this ideal. In some cases, this result...
Tauno Metsänkylä (1973)
Acta Arithmetica
Benjamin Dupuy (2007)
Acta Arithmetica
R. J. Stroeker (1979)
Compositio Mathematica
Dragan Stankov (2008)
Publications de l'Institut Mathématique
Joshua Harrington, Lenny Jones (2013)
Colloquium Mathematicae
Let , where . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of on the coefficients of f(x) is the best possible in this situation.
Claude Levesque (1977)
Manuscripta mathematica
Andrzej Schinzel (1991)
Mathematica Slovaca
Cristian D. Popescu (2006)
Journal de Théorie des Nombres de Bordeaux
In this paper, we give the complete characterization of the –torsion subgroups of certain idèle–class groups associated to characteristic function fields. As an application, we answer a question which arose in the context of Tan’s approach [6] to an important particular case of a generalization of a conjecture of Gross [4] on special values of –functions.
J. Brzezinski (1989)
Journal für die reine und angewandte Mathematik
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