We obtain good estimates on the ranks of universal quadratic forms over Shanks' family of
the simplest cubic fields and several other families of totally real number fields. As the main …

This book is an elementary introduction to $ p $-adic analysis from the number theory
perspective. With over 100 exercises included, it will acquaint the non-expert to the basic …

Let $ p $ be a fixed prime number. Let $ K $ be a totally real number field of discriminant $
D_K $, and let $\mathcal {T} _K $ be the torsion group of the Galois group of the maximal …

Families of cyclic cubic fields - ScienceDirect Skip to main contentSkip to article Elsevier logo
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A family of cyclic cubic polynomials whose roots are systems of fundamental units - ScienceDirect
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We consider, for real abelian fields K, the Birch--Tate formula linking the tame kernel\# K\_2
(Z\_K) to $\zeta $\_K (-1); we compare, for quadratic and cyclic cubic fields with p= 2, 3,\# …

1. Introduction. Let ϵ be a cubic algebraic unit. Let Πϵ (X)= X3− aX2+ bX− c∈ Z [X], with
c∈{±1}, be its minimal polynomial. Let ϵ, ϵ and ϵ be the three conjugates of ϵ, ie the three …

We are interested in solving the congruences f 3+ g 3+ 1≡ 0 (mod fg) and f 4− 4 g 2+ 4≡ 0
(mod fg) in polynomials f, g with rational coefficients. Moreover, we present results of …

$ A^{*}(k) $($ k $ 上の群多様体の $ k $-有理点のなす群) であることに意味がある.
複素数の場合にはノノレム写像の**方根が通常の絶対値として $\mathrm {R} $ 上定義されるので …

A parametric family of cubic Thue equations Page 1 http://www.elsevier.com/locate/jnt Journal
of Number Theory 107 (2004) 63–79 A parametric family of cubic Thue equations Alain …