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Büchi Sequences in Local Fields and Local Rings

Jerzy Browkin — 2010

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that there exist infinite Büchi i sequences in some local rings and local fields, with the exception of the ring p of p-adic integers. In p there are only finite but arbitrarily long Büchi sequences.

Refined Kodaira classes and conductors of twisted elliptic curves

We consider elliptic curves defined over ℚ. It is known that for a prime p > 3 quadratic twists permute the Kodaira classes, and curves belonging to a given class have the same conductor exponent. It is not the case for p = 2 and 3. We establish a refinement of the Kodaira classification, ensuring that the permutation property is recovered by {refined} classes in the cases p = 2 and 3. We also investigate the nonquadratic twists. In the last part of the paper we discuss the number of isogeny...

On Exceptions in the Brauer-Kuroda Relations

Jerzy BrowkinJuliusz BrzezińskiKejian Xu — 2011

Bulletin of the Polish Academy of Sciences. Mathematics

Let F be a Galois extension of a number field k with the Galois group G. The Brauer-Kuroda theorem gives an expression of the Dedekind zeta function of the field F as a product of zeta functions of some of its subfields containing k, provided the group G is not exceptional. In this paper, we investigate the exceptional groups. In particular, we determine all nilpotent exceptional groups, and give a sufficient condition for a group to be exceptional. We give many examples of nonnilpotent solvable...

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