Fundamental units of real quadratic fields of odd class number
نویسندگان
چکیده
منابع مشابه
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...
متن کاملComputation of p-units in ray class fields of real quadratic number fields
Abstract. Let K be a real quadratic field, let p be a prime number which is inert in K and let Kp be the completion of K at p. As part of a Ph.D. thesis, we constructed a certain p-adic invariant u ∈ K× p , and conjectured that u is, in fact, a p-unit in a suitable narrow ray class field of K. In this paper we give numerical evidence in support of that conjecture. Our method of computation is s...
متن کاملElliptic units in ray class fields of real quadratic number fields
Let K be a real quadratic number field. Let p be a prime which is inert in K. We denote the completion of K at the place p by Kp. Let f > 1 be a positive integer coprime to p. In this thesis we give a p-adic construction of special elements u(r, τ) ∈ K× p for special pairs (r, τ) ∈ (Z/fZ)× × Hp where Hp = P(Cp)\P(Qp) is the so called p-adic upper half plane. These pairs (r, τ) can be thought of...
متن کاملOn a Class Number Formula for Real Quadratic Number Fields
For an even Dirichlet character , we obtain a formula for L(1;) in terms of a sum of Dirichlet L-series evaluated at s = 2 and s = 3 and a rapidly convergent numerical series involving the central binomial coeecients. We then derive a class number formula for real quadratic number elds by taking L(s;) to be the quadratic L-series associated with these elds.
متن کاملComputation of Real Quadratic Fields with Class Number One
A rapid method for determining whether the real quadratic field Sí = S(\/D) has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of .W and then uses the Generalized Riemann Hypothesis to rapidly estimate L(l, x) to the accuracy needed for determining whether or not the class number of 3£ is one. The results of running this algor...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2014
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.10.019