Distribution of fundamental units of real quadratic number fields(Algorithmic Number Theory and Its Applications, <Special Issue> Joint Symposium of JSIAM Activity Groups 2007)

Abstract

Let p be a prime number which satisfies p ≡ 1(mod 4). Let ε_p=t_p+u_p√<p>/2>1 be the fundamental unit of the real quadratic number field Q(√<p>). In this note, we study some distributions of t_p, u_p from a few viewpoints. For all computations in this paper, we used PARI/GP.