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Currently displaying 1 – 4 of 4

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On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties.

Noboru Aoki — 1984

Mathematische Annalen

On Some Arithmetic Problems Related to the Hodge Cycles on the Fermat Varieties (Erratum).

Noboru Aoki — 1984

Mathematische Annalen

On Tate’s refinement for a conjecture of Gross and its generalization

Noboru Aoki — 2004

Journal de Théorie des Nombres de Bordeaux

We study Tate’s refinement for a conjecture of Gross on the values of abelian $L$ -function at $s = 0$ and formulate its generalization to arbitrary cyclic extensions. We prove that our generalized conjecture is true in the case of number fields. This in particular implies that Tate’s refinement is true for any number field.

On the Tate-Shafarevich group of semistable elliptic curves with a rational 3-torsion

Noboru Aoki — 2004

Acta Arithmetica

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