Units in real cyclic fields

On the existence of Minkowski units in totally real cyclic fields

Let K be a totally real cyclic number field of degree n that is the product of two distinct primes and such that the class number of the n-th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for K.

Elliptic units for real quadratic fields

1. A review of the classical setting 2. Elliptic units for real quadratic fields 2.1. p-adic measures 2.2. Double integrals 2.3. Splitting a two-cocycle 2.4. The main conjecture 2.5. Modular symbols and Dedekind sums 2.6. Measures and the Bruhat-Tits tree 2.7. Indefinite integrals 2.8. The action of complex conjugation and of Up 3. Special values of zeta functions 3.1. The zeta function 3.2. Va...

Elliptic units of cyclic unramified extensions of complex quadratic fields

On the real quadratic fields with certain continued fraction expansions and fundamental units

The purpose of this paper is to investigate the real quadratic number fields $Q(sqrt{d})$ which contain the specific form of the continued fractions expansions of integral basis element  where $dequiv 2,3( mod  4)$ is a square free positive integer. Besides, the present paper deals with determining the fundamental unit$$epsilon _{d}=left(t_d+u_dsqrt{d}right) 2left.right > 1$$and  $n_d$ and $m_d...

Gross–Stark units for totally real number fields